One thing science can't prove is that something is endless.  It can prove something is finite by finding its edge or boundary, but if it is endless there is no boundary to be found -- except it could still be over the next hill.

Presented with a being claiming to be infinite, we would have the same problem -- we could prove it false if we found or showed how there had to necessarily be a boundary, but absent doing this we still could not be sure the being was telling the truth, since the boundary could exist but be out or our range.

Mathematical infinities are different.  Irrational numbers, for example, are decimals that go on without end.  The "density" of the number line is infinite.  And, of course, the counting numbers are endless, as well as things like the number of primes -- it isn't that we haven't found a largest prime but that we have a logical proof that such a number would be self-contradictory.  Indeed, in spite of this, we also know that there are "sizes" of infinite sets.  Heaven forbid by getting into that, but it shows to me that mathematics and reality are not the same.

This is an area, then, where I think there is a massive difference between the "real" world and the thing we have invented called mathematics.