Problems understanding some cosmological models

There are some cosmological models (for example, the pre-big bang model, the emergent model, or the string gas model) that for me, as a student, are completely incomprehensible physically and intuitively, although mathematically, they seem to have no problems. In these models, some cosmology (Minkowski space filled with whatever field or string gas on some background) exists for an infinite time before it bounces into our known universe.

And I do not understand at all what does "there is an infinite time before bounce" mean? It is clear that if you go towards the past, starting from the big bang, then you can move in the temporal direction as long as you like (this is the meaning of the -∞ sign). But the universe, which existed indefinitely before the rebound, moved not backward in time, but forward in time. If there were a clock in such a universe (or in a string gas), their hands would complete an infinite number of full circles before bouncing into our universe. How is this to be understood? In my understanding, this is equivalent to reaching an infinitely distant point in space.