Who is the person who passes in front of the narrator on the automated walkway?

There are actually six scenes/flashes where we see Brad Pitt before The Narrator meets him on the plane. A list of them has been compiled here.

The reasoning behind this is covered well in an IMDb FAQ:

As astute viewers will have observed, Tyler Durden appears in the film six times prior to the scene where The Narrator meets him on the plane. Four of these appearances are single-frame flashes, which director David Fincher refers to on his DVD commentary as "subliminal Brads" (a single frame is 1/24 of a second in duration, just slow enough for the human eye to register). The first subliminal Brad appears while The Narrator is standing at the photocopier at work, trying to stay awake; the second appears as the doctor (Richmond Arquette) tells The Narrator that to see what real pain is, he needs to attend the testicular cancer support group; the third as the support group leader (George Maguire) makes his opening remarks; and the fourth as The Narrator watches Marla Singer (Helena Bonham Carter) walk down an alley. Durden's fifth and sixth appearances are not single-frame flashes but cameo appearances: he is the furthest waiter on the right in the hotel welcome video and a passerby on a walkway in an airport.

On his DVD commentary track, David Fincher explains that the idea behind the subliminal Brads was to convey a sense of exasperation on the part of Tyler Durden; it is as if The Narrator has already created Tyler, but is hesitating to release him. The subliminal Brads are an attempt to illustrate Tyler's frustration with The Narrator -- if The Narrator would simply allow him free reign, Tyler could tackle many of the problems holding The Narrator back. Significantly, all four subliminal Brads appear at times of stress, as if Tyler is choosing these precise moments to remind The Narrator that a solution is within his grasp, he just needs to follow through with it.

Response to a comment: As for why Tyler is the way he is, consider the following dialogue from the movie in a conversation between Durden and The Narrator:

Tyler Durden: You were looking for a way to change your life. You could not do this on your own. All the ways you wish you could be, that's me. I look like you wanna look, I fuck like you wanna fuck, I am smart, capable, and most importantly, I am free in all the ways that you are not.

In other words, Durden is The Narrator's ideal, an Übermensch, a figment drawn from the latter's experiences, fantasies, and the people around him. Durden's appearance might well be similar to someone real (or it could be modelled on an actor like Brad Pitt himself who some would consider an ideal).

A model for destruction?

It is entirely possible that in the Narrator's lucid state, he was scanning the crowd subconsciously, looking for the image that would become Tyler Durden. Peering upon person to person to find the right image that would become his 'perfect' personality, the basis for his rebirth, the basis of What a man is supposed to look like.

Upon seeing this man, he was infatuated, This is Tyler, he said to himself, subconsciously. And his mind ran with it from there.

If you want to think of it in an even more meta sense, it's entirely possible the Narrator passed Brad Pitt himself and based Tyler off of Brad Pitt's image.

The Sleepwalker

The other, more accepted theory is that, as explained by Tyler towards the end, sometimes he imagines himself watching Tyler, when it is really him committing the action, speaking, etc.

It is possible that the Narrator 'thinks' he is just going his own way to the next monotonous action of his daily job ritual. But his lighter personality is actually 'asleep' and Tyler is awake and ready to start his night of mischief, mayhem, and soap-making.

It is implied that Tyler's soap business is very abundant and been running for a long time when the Narrator first 'meets' Tyler (about a year in the timeline).

It is also implied that the first time the Narrator got some sleep was when he started going to the support groups, a year later, Marla Singer crashes his party and sends him into the downward spiral into Project Mayhem.

To Sum it up

Both theories are very possible, but the more accepted one is the second.

The way it is handled in the book is very different, having the two meet on a beach, never really implying seeing any man as a 'model' for Tyler. This would imply, again, that the second is the actual explanation. Though the first does make for an interesting discussion piece.