It's technically speaking impossible to "know" that the Universe is infinite in space, as it's now understood to have a definite beginning, which means that you would have to wait around literally for ever to see the light from stars infinitely far away (this is a variation of what's called "Olber's Paradox", which asks why the night sky is dark if the Universe is infinite).
There are other, more exciting reasons than this. Assuming the Universe expands for ever then some parts of the Universe can never be seen because they are simply moving away from us too quickly for light emitted from them to ever reach us. That means that it will almost certainly be literally impossible to tell if the Universe is infinite or not.
The best we can do is to show, continually, that it is at least bigger than what we can see. In that sense, at least, current understanding certainly *is* relevant because the current understanding is that the question is open (but that it's probably infinite, for the moment).