Think of singularities as unidirectional. We don't understand what if anything was before the big bang, there is no return from inside a black hole event horizon, we don't understand what would follow after an AI singularity. That doesn't mean that they don't have a threshold in time/space/spacetime, just that crossing that threshold breaks the rules we know.

Singularities are mathematical constructs and are used to model different kinds of phenomena. Black holes and the big bang are only roughly comparable (but by no means similar) if you are considering a black hole from "inside" of one.

For blackholes it's the reverse, all paths lead to the singularity, and there is no 'after' as opposed to the big bang where all paths lead away from the singularity and there is no 'before.' If you hit rewind on a video of matter falling into a black hole's singularity, it would look like a big bang where everything was created from nothing at an infinitely dense point and starts flying outwards.