“For once you have tasted flight you will walk the earth with your eyes turned skywards, for there you have been and there you will long to return.” -Leonardo da Vinci
The Universe is an awfully big place, but how certain are we that we couldn’t travel in a straight line for a very long time and simply return to our starting position? Just because we can travel through the Universe for an arbitrarily, perhaps infinitely long distance-or-time, doesn’t mean the Universe itself is infinite. It’s quite possible that it closes in on itself, and that any straight-line path will eventually return you to your beginning.
If we wanted to test this possibility, there are a few ways to do it. The best would be to look for repeating structures at a specific distance in the Universe. While we wouldn’t recognize a younger version of our Milky Way, the large-scale structure or the cosmic microwave background would exhibit correlations if the Universe repeated on the scale of what’s observable to us.
And finally, even if we can’t see any, the Universe may still repeat on scales larger than the ones we can see, even if that renders a complete “loop” a physical impossibility.