The universe is a particular shape. One end is tightly compressed. We don;t know the shape of the other end, of which you speak.
The point is that time is this shape. We might say that today, last week, next year, the Big Bang (or Plank epoch) and the Big Crunch (or whatever) are all places in the universe, of which these three spatial dimensions are but one region. The unique string of memories in the biological computer called “myself” exists in an even more specific region called “21st Century Earth”.
Concerning my attitude toward the end of the universe, I think Woody Allen said it best in Annie Hall:
Young Alvy’s Mom: Tell Dr. Flicker.
[Young Alvy sits, his head down - his mother answers for him]
Alvy’s Mom: It’s something he read.
Doctor in Brooklyn: Something he read, huh?
Alvy: [his head still down] The universe is expanding.
Doctor: The universe is expanding?
Alvy: Well, the universe is everything, and if it’s expanding, someday it will break apart and that would be the end of everything!
Alvy’s Mom: How is that your business?
[she turns back to the doctor]
Alvy’s Mom: He stopped doing his homework!
Alvy: What’s the point?