I don’t think we know how the end of the universe even from outside of the black hole would look like. If I remember correctly at some point even black holes may evaporate due to Hawking radiation.
As for the big bang being a white whole, there are a lot of problems. Like it would mean the universe started at one point in space and that’s the opposite of what we see that the universe started everywhere.
Well, there are a lot of penguin posts here.