We think the universe goes far past or infinitely past our viewable horizon because when we measure the universe, it is flat. If you had a ball represents the universe and zoomed into the edge as far you could, that spot would appear flat. That flat spot is 1.74 million billion AU (our Hubble value) and the rest of the ball is the unobservable universe. With a system that is basically or actually infinite we know that patterns can and do repeat. Meaning yes, multiple versions of this conversation have happened or will happen eventually. If multiverse theory of quantum physics is correct, our universe, infinite or not is just peanuts compared to all the permutations that are possible.