I think the infinite universe paradox is easy to solve if you think about it in terms of the real world and not a thought experiment. In the real world reality is only what you observe, so even if you travelled in a space ship at the speed of light you will only travel a short distance. Even if you solved aging and travelled for millions of years, since the universe is expanding you will never reach the "end" of the universe, so its not physically possible. Therefore there is no such thing as infinity in reality, only as a thought experiment. That's hard to accept, but infinity exists only in our mind not in reality because we exist in time and space. If we were able to exist where there is no time and space we might be able to experience or observe infinity.