If the universe goes on forever, it goes on forever. This also means anything that could possibly happen among things that may never happen, could happen.
You see as an example, the variables creating life are so specific that if the time to get them right over and over again is infinite, so are the events of life being created.
If the universe does not go on forever, the human race would never know considering the speed of light and other complications among the fact that once we got there the stars there would probably have slowly cooled down to a dimly lit orb.