Can a puthujjana have unshakable faith in the Buddha-Dhamma?

This question is well answered by MN 27 and the commentary of its translator, Ven. Thanissaro.

According to the sutta, the one who attains the four jhanas, the knowledge of past lives/ abodes recollection and the knowledge of beings passing away and reappearing, is not yet able to come to the conclusion (i.e. have unshakable faith, or have no doubt at all) regarding the Buddha, the Dhamma and the Sangha:

"This, too, is called a footprint of the Tathagata, a scratch mark of the Tathagata, a tusk slash of the Tathagata, but a disciple of the noble ones would not yet come to the conclusion, 'The Blessed One is rightly self-awakened; the Dhamma is well-taught by the Blessed One; the Sangha of the Blessed One's disciples has practiced rightly.'

However, the sutta continues:

"With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, the monk directs and inclines it to the knowledge of the ending of the mental fermentations. He discerns, as it has come to be, that 'This is stress... This is the origination of stress... This is the cessation of stress... This is the way leading to the cessation of stress... These are mental fermentations... This is the origination of fermentations... This is the cessation of fermentations... This is the way leading to the cessation of fermentations.'

"This, too, is called a footprint of the Tathagata, a scratch mark of the Tathagata, a tusk slash of the Tathagata. A disciple of the noble ones has not yet come to conclusion, but he comes to the conclusion, 'The Blessed One is rightly self-awakened; the Dhamma is well-taught by the Blessed One; the Sangha of the Blessed One's disciples has practiced rightly.'

So, when he fully understands the four noble truths, only then does he come to the conclusion (i.e. have unshakable faith, or have no doubt at all) regarding the Buddha, the Dhamma and the Sangha. But he himself has not yet come to a conclusion, i.e. he is not yet an Arahant.

So, what is his attainment at this stage?

Ven. Thanissaro, the translator, comments:

This stage in the practice would seem to correspond to reaching stream-entry, inasmuch as one of the standard definitions of stream-entry is direct vision of the four noble truths. It is also the stage at which one reaches unwavering conviction in the Buddha, Dhamma, and Sangha.

The sentence stating that the stream-enterer has come to a conclusion without coming to conclusion is a play on words. The idiomatic expression for coming to a conclusion — ni.t.tha.m gacchati — can also mean coming to a finish, reaching completion, or coming to an end. To distinguish these two meanings, the text here uses the form ni.t.tha.ngato to mean having come to a finish, and ni.t.tha.m gacchati to mean coming to a conclusion.

That means only the one who has gained stream entry could have unshakable faith in the Buddha, the Dhamma and the Sangha.

Then the sutta goes on to describe the Arahant (who comes to a conclusion):

"His heart, thus knowing, thus seeing, is released from the fermentation of sensuality, the fermentation of becoming, the fermentation of ignorance. With release, there is the knowledge, 'Released.' He discerns that 'Birth is ended, the holy life fulfilled, the task done. There is nothing further for this world.'

"This, too, is called a footprint of the Tathagata, a scratch mark of the Tathagata, a tusk slash of the Tathagata, and it is here that a disciple of the noble ones has come to conclusion: 'The Blessed One is rightly self-awakened; the Dhamma is well-taught by the Blessed One; the Sangha of the Blessed One's disciples has practiced rightly.'"

Right view arises with two conditions:

AN2.126:1.1: “There are two conditions for the arising of right view. What two? The words of another and proper attention. These are the two conditions for the arising of right view.”

Unshakeable faith happens thus:

MN106:13.3: But sir, what is noble liberation?” “Ananda, it’s when a mendicant reflects like this: ‘Sensual pleasures in this life and in lives to come, sensual perceptions in this life and in lives to come, visions in this life and in lives to come, perceptions of visions in this life and in lives to come, perceptions of the imperturbable, perceptions of the dimension of nothingness, perceptions of the dimension of neither perception nor non-perception; that is identity as far as identity extends. This is the deathless, namely the liberation of the mind through not grasping.

Importantly, "perceptions of the imperturbable" are also identity and to be relinquished without grasping. So declaring "I am imperturbable" misses the mark. Better to just walk while walking and just stand while standing.

Decades ago I went to a retreat, perceived non-self and freaked out. That was definitely unpleasant, but it was an important clue about the Noble Truths. It's taken a lifetime to muster proper attention and find the words of another. With proper attention and the words of another, one can have faith that the Noble Eightfold Path will give rise to unshakeable faith upon release from all the fetters.