Is it possible for absolutely everyone to attain enlightenment?

No. It is not possible.

It is not possible because there are those who do not believe the first Noble Truth.

Sir, I remember that suffering is the first noble truth you’ve taught SN56.15

In not believing the first Noble Truth, they flail about, running from suffering and grasping at delights. They think suffering to be a lie and reject the truth.

It is not possible because there are those who do not believe the second Noble Truth.

the origin of suffering is the second; SN56.15

In not believing the second Noble Truth, they grow despondent, thinking suffering universal and unavoidable. They think that suffering has no origin and reject the truth.

It is not possible because there are those who do not believe the third Noble Truth.

the cessation of suffering is the third; SN56.15

In not believing the third Noble Truth, they act as they wish, careless of deed and blaming others. They think that suffering is inevitable and reject the truth.

It is not possible because there are those who do not believe the fourth Noble Truth.

and the practice that leads to the cessation of suffering is the fourth. SN56.15

In not believing the fourth Noble Truth, they follow uncertain paths, wandering astray. They reject the Noble Eightfold Path.

Also note that people do change their minds, so a particular person may come to believe in the Noble Truths. Whether they change their minds in this life is up to them.

That's my interpretation of the suttas.

The Noble Dhamma that Buddha proclaimed has the nature of Dependent Origination. With craving as the origin, suffering comes to arise. With the complete cessation of craving, the cessation of suffering (i.e. liberation/enlightenment/Nibbana). Therefore you shouldn't look for a yes-no answer.

However it sounds like what you are asking is if someone is practicing the Noble Eight Fold Path, can there be other factors that will limit their development and cause a delay in attaining nibbana? Yes there could be. One well-known case is for someone who has committed one or more of the ānantarika-kamma. That person will not have any attainment in this life.

However the most typical case for these types of questions to arise is not having heard true dhamma and not practicing according to the True Idea.

But for a person whose mind is fixed on Nibbana (i.e. having seen Noble Truths to some level, having practiced the Noble Eight Fold Path, having understood even a single link of dependent origination), for that person either in this life or in the next or within the next seven births, he will attain Nibbana.

A good place to start is by learning and practicing the Noble Eight Fold Path

With Metta

For the people who have physical limitations, they would not become enlightened in one life time. But as we know that birth and death are just concepts and in ultimate reality these things doesn't exits, it doesn't mean the being would never get enlightened. But it means it is impossible to become enlightened in the life time in which they have the physical limitations.

But that doesn't mean that the people who have the "potential" or "capacity" to attain enlightenment would get enlightened in one-life time(or maybe in millions of life-times) because there are many factors for the humans that prevents them from attaining Nibbana. One of the biggest factors is the "enjoyment of suffering". You can say it "clinging to suffering" too because clinging and enjoyment are related to eachother.

That's why the people who are Buddhist meditators(or in other spiritual traditions that is aligned with the Buddhist teaching) are very lucky because they have this chance to attain stream-entry and beyond in one life-time. And this becomes some people's reality through mindfulness and right living. This is truly a blessing and we must thank to Buddha and Buddha's disciples who carried his teachings to our times that makes some people stream-enterers, once-returners, non-returners and even Arahants and gives many others the chance to attain enlightenment.

Why it important to value Conditions?

paccantaro – living on a place where Buddha Sasana does not flourish

How could one change this situation? Change the place, or put effort so that it might flourish (which would require the understanding and the right tendency first)

micchaditthi – born/associate among people with wrong view

That goes much along what is called the pre-requisite for the wing of awakening. The admirable friend. What if there are no around, would the teaching alone help?

vitalingo--persons with congenital, defects such as idiocy, etc.

To change that situation is maybe not easy but if such a person would be integrated in a culture that goes in the right direction, he might gain a good support in simply following what others do.

... to gain right is very seldom (Great Opportunities ) and even if having the great blessings, if having killed mother, father, an Arahat, caused a Buddha shed blood, split the Sangha and holding grave wrong views, any growth is impossible, even to reach the path.

So value already accumulated conditions and seek for complement and for such it is most important to do not associate with fools, people of wrong view: How to address wrong view?.

Take care and seek for places where right view can be archived: Boarderlands

“Monks, suppose that this great earth were totally covered with water, and a man were to toss a yoke with a single hole there. A wind from the east would push it west, a wind from the west would push it east. A wind from the north would push it south, a wind from the south would push it north. And suppose a blind sea-turtle were there. It would come to the surface once every one hundred years. Now what do you think: would that blind sea-turtle, coming to the surface once every one hundred years, stick his neck into the yoke with a single hole?”...Chiggala Sutta

Now even all told by a stranger forest dweller, hardly ever to meet... but if the conditions are not there, no chance either, even if face to face to the/a Buddha.

{Not given for trade, exchange, stacks and what binds to the world but for toward liberation}

The suttas literally say it is not possible for everyone to attain enlightenment (Dhp 174; AN 10.95; MN 26). I would not concern myself with the Buddhist "Evangelists" making false promises. If it is our destiny to be enlightened, it would probably have occurred by now. Best to abandon the desire or hope for enlightenment. The more abandonment of desire & hope that occurs, the greater the possibly of possibly reaching enlightenment. Right View has only one purpose - namely - to direct the mind to abandoning desire & hope. Ajahn Buddhadasa said Nibbana is the 'absence of hope'.

Blind is the world; here only a few possess insight. Only a few, like birds escaping from the net, go to realms of bliss

Dhp 174

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And, Master Gotama, when having directly known it, you teach the Dhamma to your disciples for the purification of beings, for the overcoming of sorrow & lamentation, for the disappearance of pain & distress, for the attainment of the right method, & for the realization of Unbinding, will all the cosmos be led [to release], or a half of it, or a third?"

When this was said, the Blessed One was silent.

AN 10.95

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I surveyed the world with the eye of an Awakened One. As I did so, I saw beings with little dust in their eyes and those with much, those with keen faculties and those with dull, those with good attributes and those with bad, those easy to teach and those hard, some of them seeing disgrace & danger in the other world.

MN 26

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58. Upon a heap of rubbish in the road-side ditch blooms a lotus, fragrant and pleasing.

59. Even so, on the rubbish heap of blinded mortals the disciple of the Supremely Enlightened One shines resplendent in wisdom.

Pupphavagga

The nature of mind is clear light, defilements are only adventitious.

-- Dharmakirti

In my view, enlightenment is possible -- if not within this lifetime, then in other lifetimes.

From the point of view of the doctrine of Buddha Nature, all sentient beings possess the inherent seed for enlightenment. The Dalai Lama says:

Every sentient being—even insects—have Buddha nature. The seed of Buddha means consciousness, the cognitive power—the seed of enlightenment. That’s from Buddha’s viewpoint. All these destructive things can be removed from the mind, so therefore there’s no reason to believe some sentient being cannot become Buddha. So every sentient being has that seed.

Logically, karma must have fruition, and the mindstream follows the path of Samsara endlessly until it reaches Nirvana. Otherwise, it will always reincarnate, experiencing karma in the process. All karma is impermanent, as Buddhism suggests. From these premises, any karma -- negative or positive -- must come to an end. Even individuals having committed much negative karma, as Milarepa or Angulimala, reached high levels of spiritual capacity.

As to your question more specifically, for individuals cognitively impaired, such individuals may develop merit within their lifetimes, which will help them in future lives, even if they don't follow the path in its entirety.

To perceive this lifetime and the next as fully separate is against the idea of dependent origination, entailing linkage between cause and consequence. From the view of emptiness, the division of this life and the next -- as well as many other such divisions -- is empty of intrinsic nature: it exists on the basis of appearance alone. Merit, from this point of view, is indistinct from the realization of the spiritual path; the Buddha committed many compassionate acts in previous lives which furthered his enlightenment.

Therefore, from the view of the two truths of Nagarjuna, merit is karmically linked with enlightenment, on the basis of conventional reality's cause and effect. In other words, merit furthers enlightenment, and can be developed by individuals incapable of deeper cognition.

From the point of view of ultimate reality, in the same framework, I recall visiting a Buddhist temple where a Tibetan master explained how emptiness entails a division into parts. Even if a person cannot fulfill enlightenment in this lifetime, they can contribute to it in by right deeds, and even with very partial deeds. If compassion meditation consists in various altruistic intentions towards others, then why not a few intentions? Even one intention? Anything a person is capable of may fulfill a virtuous purpose.

For someone unable to commit any action on the basis of great disease or such things, then their life may consist in experiencing negative karma accumulated previously. In diminishing this karma they also promote later enlightenment.

In sum, I suggest enlightenment should be perceived in the context of multiple lifetimes. Otherwise, many individuals might conclude it is not possible for them, and commit detrimental acts. They would be forgetting the wholeness which the Buddhist path possesses.

P.S.: Isn't it that even for people deficient in a cognitive sense, that their minds still possess the capacity for virtuous and detrimental acts? Any mind entails various possibilities, leading either towards or away from enlightenment. And if a person failed to have the capacity of choice, i.e. the capacity for intention, then I'm unsure how this lack of intention would arise karmically speaking. In any case, I wish this helps!