How can that happen? If you give me any answer to anything, I can ask why that thing.
Because I want to. Because I'm curious? Is there a point you were actually trying to make or did you just think that was a clever answer? It wasn't.
You brought in intentionality. We have sophisticated brains, which we can, and do use. There is no reason at all to think that anything we can think of to question is because we are intended to find the answer.
Which just emphasises that you don't understand the point. There is no "self-generated" about it. There is no generation. The space-time didn't "come from" anything. It just is. That's why the physical universe is self-contained and has no obvious need for anything else.
The view of (space-)time that modern science accepts is counterintuitive and can be difficult to grasp, but you (and so many other theists and those who cling to intuition) don't seem to even want to try to understand.
No, you just need to relinquish your precious human inuition, and accept the perfectly self-consistent, mathematically (and therefore logically) well formed modern view, in which the question of "generation" (a time-based concept) does not arise.
Don't get me wrong, there is still a question, and you can have your mystery of existance, it's just that there is no point in looking for some logical gap in the current notion of physical existance that you can point to and say "this can't be explained in physical terms". There is no something happening to nothing to make a something, there is no relevance to whether time is finite or infinite in the past (it doesn't matter either way).
All you have is a "why does this exist, not something else or nothing?", not "where did all this come from?", or "how was it generated?"