They have gone into a different, branching, alternate timeline. There is no reason to believe that Stark would remember this event unless he (or the audience) also know that this event also unfolded in exactly the same way in Stark's past (like if it was shown in a previous movie).
Related dialogue (emphasis mine):
Bruce Banner: Changing the past doesn't change the future.
Scott Lang: Look, we go back, we get the stones before Thanos gets
them. Thanos doesn't have the stones. Problem solved.
Nebula: That's not how it works.
Bruce Banner: If you travel to the past, that past becomes your future, and your former present becomes the past, which can't now be changed by your new future.
Scott Lang: So Back to the Future is a bunch of bullshit?
As explained by Banner, and as remarked upon by Lang, their actions when they went back to the past (new future) didn't and won't affect their former present (past), so none of them would've "remembered" what happened because those events didn't happen or didn't happen in the exact same way as their past.
We don't know if the Hulk arrived on the ground floor in the same manner and at exactly the same time as the original timeline. We don't know if he even went down the stairs at all because the events shown in Endgame are already after they've arrived in the past (the timeline has already branched).
Thor "remembered" that his mother would die on that day they came back to in the past because this event was shown in Thor: The Dark World. The events: Hulk busting out of the stairwell, past Stark and Thor arguing with Alexander Pierce, among other events, were only shown in Endgame, and not in a previous movie. I've re-watched The Avengers (2012) to verify and those events were not shown in that movie.
In his memoir, Look Out For The Little Guy! Scott Lang (Ant-Man) confirms that they traveled to alternate timelines to collect the Infinity Stones. He writes in Chapter 10: From beginning to endgame:
The idea was, we would identify specific, recent points on alternate timelines where we knew an Infinity Stone to be. And then we’d use the Quantum Tunnel to “jump” to that timeline and grab the stone there. Once in possession of all six, we would have the same power Thanos used to create the Blip—except we’d use that power to bring everyone back.
Unfortunately, once my Tony grabbed the Tesseract case, the Hulk emerged from the stairwell and knocked Tony down. But not my Hulk, the other Hulk. The one from 2012…but, like, an alternate 2012. You know what, let’s call him “Alt-2012 Hulk.”
Alt-2012 Hulk knocked Tony over, the case slid across the floor, and in the end all my distraction did was allow Alt-2012 Loki to escape with the Space Stone. One can only imagine what that led to.
That’s when I uttered a phrase that may as well describe my entire life:
“That wasn’t supposed to happen, was it?”
In other MCU media:
Loki (2021 TV series) expounds on the concept of branching timelines. In Loki, it was revealed that the Loki that took the Tesseract in Endgame is a variant of Loki from a branched timeline and that a person may have multiple variants of themselves, each from their own timelines. From this, it stands to reason that "past" Stark is a variant of the time-traveling "original" Stark. Time-traveling Stark would not have memories of his other variants' experiences, just like Loki didn't have memories of his other variants' experiences.
In Doctor Strange in the Multiverse of Madness (2022), where Strange travels the multiverse and learns of and meets his variants, it was revealed that the Strange variants in the other universes have very different experiences of their pasts and even have very different personalities from the "original" Doctor Strange. Aside from very few, specific experiences, Doctor Strange did not "remember" his other variants' experiences.