Last I heard scientists were leaning more toward the ever-accelerating expansion “heat death” theory then the expansion-to-contraction “big crunch” theory, but it’s not set in stone yet. But even if “big crunch” came out on top, assuming that the life of the universe is cyclical is pure conjecture. It could be right, but it’s unprovable, so we’ll never know.

As for the existence of space-time before the big bang, I don’t know what to tell you, I’m just quoting theory. By definition, the big bang is when space-time came to be. If the big bang was the result of an ancestor universe’s big crunch, we can’t assume that the same space-time carried over, let alone that the ancestor universe even had something analogous to space-time. Barring some insanely massive breakthrough, it’s simply unknowable.