I had a layman's question about black holes. The singularity is infinitely dense, and approaching it involves approaching the C asymptote, which in turn slows d

I had a layman's question about black holes. The singularity is infinitely dense, and approaching it involves approaching the C asymptote, which in turn slows down time more and more and more. Is it possible that the universe could actually end before you hit the singularity? Like the time slowdown becomes so severe that you actually witness the heat death of the universe and the merging of all black holes before you actually hit the center? I've always wondered what would happen if you fell into a black hole and hit the singularity, and recently the thought occurred to me that it is simply physically impossible to actually get there.