Tony Berard's refutation below misses the point. You (Joe) have made a logical error. You state (correctly) that infinity can never be reached. You draw the conclusion that infinity "goes on forever", which is mathematically meaningless, so your conclusion that there is "no room for another infinity" is also meaningless. As Berard pointed out in his first response, mathematicians have understood that there are different infinities which are of different orders. I'll restate his case, but look at Cantor (https://en.wikipedia.org/wiki/Georg_Cantor) for more detail. Briefly, there are an infinite number of integers (countable numbers). But between any pair of integers there are an infinite number of UNcountable numbers. Clearly then, the uncountable numbers form a larger infinite set than the countable numbers.

Does this prove that an infinitely powerful god does not exist? I would say not (and I am functionally an atheist myself) as the "infinite" in the concept of an infinitely powerful god is used in an informal, non-matehmetical, sense. In a way, Berard is making a similar error as you have made.