How do we know they're still alive & the world didn't end? Because the opening of 1.01 proved it to us.
In S2, Jim finds the text of the Good Omens novel within the bookshop, as an unpublished book that Aziraphale wrote. This scene, and the opening of 1.01, can explain the ending of S3.
Even if, like I do, you think this scene of Jim finding the book is part of Aziraphale's dream? Aziraphale still has to have written this book in reality within Good Omens because that was already suggested by all of our copies of the novel in our world long before the tv series. All of our copies all have an acknowledgement to Crowley at the start but not to Aziraphale, which is just one of the many Clues in the novel showing that Aziraphale is meant to have written the book within the world of Good Omens. Thing is, though...
The Jim scene in S2 shows us that, within the world of Good Omens? The book is currently unpublished and missing a crucial piece of front matter. We watch Jim flip through the empty pages at the front of the book so that we'll see this for sure. It's missing the true first bit of text in the novel-- The Caveat on the copyright page. That Caveat? Has plenty of other layers of meaning but it's also a short warning against a plot that now seems a bit familiar after the end of S3 and which was already referenced in S1: Causing Armageddon can be dangerous. Do not attempt it in your own home.
Those lines are actually the beginning of the opening of Good Omens in 1.01-- so we already know that they do eventually exist within the world of Good Omens itself... a world where The Voice of God's monologue that opened the series (and everything else she says) is all from the text of the novel that, within this world, Aziraphale wrote.
The story we've been watching all along? It already included The Caveat that we haven't yet seen added into the text, in such a way that it makes us know for sure that it eventually is added into it...
That can only happen if Aziraphale is there to write it.
That can only happen if the world didn't actually end.
That can only happen if S2 & S3 in the present were Aziraphale's dream, the way that the final shot of S3 shows us is the case. Aziraphale hadn't yet lived through the dream that inspired The Caveat... He just did, though. That's what we were watching.
On the other side of this nightmare, one thing that Aziraphale will do will be to finish and publish that book that we call Good Omens and, in doing so, he'll add that warning against causing Armageddon in your own home. We know that Aziraphale will because we've seen that he does in the future-- that's how we got the very first thing that we ever saw: the opening of 1.01. The beginning of S1-- the start of the story? It was there, in part, to help us understand the ending.
