How could one know that Nibbana is the cessation of consciousness if there is no consciousness?

I am assuming you are referring to a passage in the Heart Sutra:

Shariputra, form does not differ from emptiness, emptiness does not differ from form. That which is form is emptiness, that which is emptiness form. The same is true of feelings, perceptions, impulses, consciousness.

Shariputra, all dharmas are marked with emptiness; they do not appear or disappear, are not tainted or pure, do not increase or decrease. Therefore, in emptiness no form, no feelings, perceptions, impulses, consciousness.

No eyes, no ears, no nose, no tongue, no body, no mind; no color, no sound, no smell, no taste, no touch, no object of mind; no realm of eyes and so forth until no realm of mind consciousness. No ignorance and also no extinction of it, and so forth until no old age and death and also no extinction of them. No suffering, no origination, no stopping, no path, no cognition, also no attainment with nothing to attain.

Emptiness in this Sutra refers not to nothingness, but to the opposite: the interdependence of all phenomena, both mental and physical. There is some discussion among scholars on whether the sutra originated in China or India, to answer your question I'll use the Chinese/Japanese characters.

In Chinese and Japanese, emptiness is often represented by the character mu 無, which also means "no" or "negative". We don't have an exact equivalent in English for mu, so the Sutra loses something of its inner meaning by just using "no".

The sutra is not stating that there is "no X in Y" but inferring that X = Y. Otherwise said, there is no such thing as "consciousness" that is independently existing, it is a manifestation of emptiness.

The sutra goes on giving some examples that are linked to consciousness: sight, hearing, smell, etc. These examples refer to the state of mind where one would "listen, but not hear" as they say in Zen: that is, the senses function, but the mind does not name the perceptions. It's like saying: "sense it, but don't name it in your head". Because once you name it, it's no longer the perception, but your mental interpretation of the perception. This is what is meant in Mahayana by the expression "emptiness is the mother of ten thousand named things".

It seems to me that theoretically one could see the no consciousness of Nibbana from a point in time i.e. from "outside" no consciousness but looking into no consciousness.

The seeing would have to be "supramundane" though because otherwise it would be mere fantasy.

One would need to make sure that the seeing isn't delusion.

Note: I am not denying that there is also the "experience" of no consciousness from "inside".

Here's a Mahayana explanation.

I suppose you were thinking about the twelve nidanas and how the whole chain, including vijnana, ceases with cessation of ignorance?

Please know that "vijnana" is strictly speaking not consciousness. That's a very approximate translation. Depending on context vijnana should be translated as either "experience of world and the objects" or more technically as "semiosis".

Please look up this word. Semiosis means interpretation of signs into their meanings. Like when you hear a certain sound and you recognize that as e.g. barking of dog. This is the foundation of all (regular, unenlightened) mental processes, they all have semiosis at the bottom.

But enlightened mind does not function like that. It is capable of semiosis as a kind of "backward compatibility mode" but that's not its main modus operandi.

Enlightened mind's state is not discrete. It's not prone to jumping to conclusions. When it hears what you recognize as "barking of dog" it takes that as information that may potentially have a number of interpretations but it doesn't conclude on any of them, it keeps its options open. It never concludes on an interpretation and that's exactly why it never gets out of sync, and that is why it's not subject to suffering.

Enlightened mind is not "vijnana". When ignorance ends, "vijnana", the crude semiotic mind, dissolves. At that time the fundamental mind of enlightenment ("rigpa" in Tibetan) that has always been there is no longer obscured by the discrete forms of regular mind. The mind of enlightenment is not unconscious - it knows everything the regular mind knew, and more. It's just a different kind of knowledge, formless interconnected simultaneous knowledge ("prajna") - as opposed to the crude "this means that" of semiosis.

So there's no contradiction. When ignorance ends - vijnana ends and the primordial clarity known as rigpa or prajna is unveiled. This clarity is what "knows" the cessation of regular mind.

I will explain sutta expression & a classical Theravadin take on this first.

“This, bhikkhu, is a designation for the element of Nibbāna: the removal of lust, the removal of hatred, the removal of delusion. The destruction of the taints is spoken of in that way.”

The Arahant is fully released from greed, anger & delusion and it is called Nibbana with residue on account of the absence of delusion, greed & anger.

Is this the only way the word Nibbana is used? No it's not the only way.

“Reverend, they speak of ‘extinguishment in the present life’. In what way did the Buddha speak of extinguishment in the present life?”

“First, take a mendicant who, quite secluded from sensual pleasures … enters and remains in the first absorption. To this extent the Buddha spoke of extinguishment in the present life in a qualified sense. …

Furthermore, take a mendicant who, going totally beyond the dimension of neither perception nor non-perception, enters and remains in the cessation of perception and feeling. And, having seen with wisdom, their defilements come to an end. To this extent the Buddha spoke of extinguishment in the present life in a definitive sense.” https://suttacentral.net/an9.51/en/sujato

Note here that cessation of perception & feeling attainment is that by seeing which defilements come to an end.

It is said that cessation of perception & feeling attainment is on the treshold of Nibbana and one is then absorbed in dependence on nibbananirodha principle.

When a monk has emerged from the cessation of perception & feeling, three contacts make contact: contact with emptiness, contact with the signless, & contact with the undirected."[3]

[3] Emptiness, the signless, & the undirected are names for a state of concentration that lies on the threshold of Unbinding. They differ only in how they are approached. According to the commentary, they color one's first apprehension of Unbinding: a meditator who has been focusing on the theme of inconstancy will first apprehend Unbinding as signless; one who has been focusing on the theme of stress will first apprehend it as undirected; one who has been focusing on the theme of not-self will first apprehend it as emptiness.

There are, monks, three unskilled ways of thought: thoughts of lust, thoughts of ill-will, thoughts of hurting. And these three unskilled states disappear utterly in him whose heart is well established in the four foundations of mindfulness, or who practices concentration on the signless. - sn22.080

"His consciousness, while carrying on the practice of bringing to mind (i.e., noticing), passes beyond the continuous occurrence of phenomena and alights upon non-occurrence. One who, having practiced in the correct manner, has alighted upon non-occurrence, O king, is said to have realized Nibbana." - Questions of King Milinda

71. And here the signless liberation should be understood as the noble path that has occurred by making Nibbána its object through the signless aspect. For that path is signless owing to the signless element having arisen, and it is a liberation owing to deliverance from defilements.34 In the same way the path that has occurred by making Nibbána its object through the desireless aspect is desireless. And the path that has occurred by making Nibbána its object through the void aspect is void. - Vsm

As to OP actual question

How could one know that Nibbana is the cessation of consciousness if there is no consciousness?

This is analogical to these questions posed to the Buddha

There is the case, Ananda, where the monk would be percipient in this way: 'This is peace, this is exquisite — the resolution of all fabrications; the relinquishment of all acquisitions; the ending of craving; dispassion; cessation; Unbinding.' It's in this way that a monk could have an attainment of concentration such that he would neither be percipient of earth with regard to earth, nor of water with regard to water, nor of fire... wind... the dimension of the infinitude of space... the dimension of the infinitude of consciousness... the dimension of nothingness... the dimension of neither perception nor non-perception... this world... nor of the next world with regard to the next world, and yet he would still be percipient." https://www.accesstoinsight.org/tipitaka/an/an10/an10.006.than.html

"Friend Sariputta, could a monk have an attainment of concentration such that he would neither be percipient of earth with regard to earth, nor of water with regard to water, nor of fire... wind... the dimension of the infinitude of space... the dimension of the infinitude of consciousness... the dimension of nothingness... the dimension of neither perception nor non-perception... this world... nor of the next world with regard to the next world, and yet he would still be percipient?"

"Yes, friend Ananda, he could..."

"But how, friend Sariputta, could a monk have an attainment of concentration such he would neither be percipient of earth with regard to earth... nor of the next world with regard to the next world, and yet he would still be percipient?"

"Once, friend Ananda, when I was staying right here in Savatthi in the Blind Man's Grove, I reached concentration in such a way that I was neither percipient of earth with regard to earth... nor of the next world with regard to the next world, and yet I was still percipient."

"But what, friend Sariputta, were you percipient of at that time?"

"'The cessation of becoming — Unbinding — the cessation of becoming — Unbinding': One perception arose in me, friend Ananda, as another perception ceased. Just as in a blazing woodchip fire, one flame arises as another flame ceases, even so, 'The cessation of becoming — Unbinding — the cessation of becoming — Unbinding': One perception arose in me as another one ceased. I was percipient at that time of 'The cessation of becoming — Unbinding.'" https://www.accesstoinsight.org/tipitaka/an/an10/an10.007.than.html

Or these variants

Ven. Sariputta was staying near Rajagaha in the Bamboo Grove, the Squirrels' Feeding Sanctuary. There he said to the monks, "This Unbinding is pleasant, friends. This Unbinding is pleasant."

When this was said, Ven. Udayin said to Ven. Sariputta, "But what is the pleasure here, my friend, where there is nothing felt?"

"Just that is the pleasure here, my friend: where there is nothing felt. https://www.accesstoinsight.org/tipitaka/an/an09/an09.034.than.html

There is the case where a monk, with the complete transcending of the dimension of neither perception nor non-perception, enters & remains in the cessation of perception & feeling. This is another pleasure more extreme & refined than that. Now it's possible, Ananda, that some wanderers of other persuasions might say, 'Gotama the contemplative speaks of the cessation of perception & feeling and yet describes it as pleasure. What is this? How can this be?' When they say that, they are to be told, 'It's not the case, friends, that the Blessed One describes only pleasant feeling as included under pleasure. Wherever pleasure is found, in whatever terms, the Blessed One describes it as pleasure.'" https://www.accesstoinsight.org/tipitaka/mn/mn.059.than.html

It is said that one who attains cessation of perception & feeling gets the "dhamma eye" and sees with wisdom due to the exceptionally clear faculties of a person who is released in dependence on it.

It is not experienced through what can be grasped with wrong view to be the mind/consciousness or senses of a person.

There is a direct knowing of that which is not experienced through the allness of the all. It's not like losing consciousness, it's a different mode of reality which is the cessation principle of what is thought of as mundane reality.

Rather than thinking that consciousness cognizes it's own cessation, think that talking about consciousness only goes as far as the conditioned element goes.

The conditioned element is that which changes as it persists. We can think about it and make philosophical models of how it works in terms of consciousness & whatnot.

The cessation of the conditioned element is known to be an altogether different reality which persists without change.

Nothing comes out of the conditioned nor does anything having grasped the conditioned comes to grasp/experience the unconditioned, rather the conditioned ceases to persists and that truth & reality of cessation persists without change in it's place & is not thought of in terms of consciousness etc (terms pertaining to the understanding of the conditioned).

The conditioned having been ceases and with that all modes of being cease and there is then a freedom from being & a freedom to be anything whilst not being anything.

There are, Ānanda, these two elements: the conditioned element and the unconditioned element. Bhikkhus, there are these three characteristics that define the conditioned. What three? An arising is seen, a vanishing is seen, and its alteration while it persists is seen. These are the three characteristics that define the conditioned. The born, come-to-be, produced, The made, the conditioned, the transient, Conjoined with decay and death, A nest of disease, perishable, Sprung from nutriment and craving's cord — That is not fit to take delight in.

There are, Ānanda, these two elements: the conditioned element and the unconditioned element.

“Bhikkhus, there are these three characteristics that define the unconditioned. What three? No arising is seen, no vanishing is seen, and no alteration while it persists is seen. These are the three characteristics that define the unconditioned.” "There is, bhikkhus, a not-born, a not-brought-to-being, a not-made, a not-conditioned. If, bhikkhus, there were no not-born, not-brought-to-being, not-made, not-conditioned, no escape would be discerned from what is born, brought-to-being, made, conditioned. But since there is a not-born, a not-brought-to-being, a not-made, a not-conditioned, therefore an escape is discerned from what is born, brought-to-being, made, conditioned." The escape from that [from the conditioned], the peaceful, beyond reasoning [beyond objectification], Constant, The not-born, the unproduced, The sorrowless state that is void of stain, The cessation of states associated with suffering, The stilling of the conditioned — bliss.

There is, bhikkhus, that base where there is no earth, no water, no fire, no air; no base consisting of the infinity of space, no base consisting of the infinity of consciousness, no base consisting of nothingness, no base consisting of neither-perception-nor-non-perception; neither this world nor another world nor both; neither sun nor moon. Here, bhikkhus, I say there is no coming, no going, no staying, no deceasing, no uprising. Not fixed, not movable, it has no support. Just this is the end of suffering

Nibbana is experienced when the mind (including consciousness) is free of defilements. So, there is no permanent cessation of consciousness for the living arahant, unless you mean the cessation of defiled consciousness.

This is also known as Nibbana element with residue left or Unbinding property with fuel remaining, from Iti 44. The residue or fuel remaining refers to the undefiled aggregates including consciousness.

Ven. Thanissaro's commentary on Iti 44:

With fuel remaining (sa-upadisesa) and with no fuel remaining (anupadisesa): The analogy here is to a fire. In the first case, the flames are out, but the embers are still glowing. In the second, the fire is so thoroughly out that the embers have grown cold. The "fuel" here is the five aggregates. While the arahant is still alive, he/she still experiences the five aggregates, but they do not burn with the fires of passion, aversion, or delusion. When the arahant passes away, there is no longer any experience of aggregates here or anywhere else.

Or do you mean Nirodha Samapatti? In this state, the person entering Nirodha Samapatti would have temporary complete cessation of consciousness.

Nirodha Samapatti:
'attainment of extinction' (S. XIV, 11), also called saññā-vedayita-nirodha, 'extinction of feeling and perception', is the temporary suspension of all consciousness and mental activity, following immediately upon the semi-conscious state called 'sphere of neither-perception-nor-non-perception' (s. jhāna, 8).