Presupposition of the question. The question, "Does X exist?" is either trivial or empty. On the one hand, as Hume said one time, it seems as if in thinking of something, I always think of it as existing (if only in thought). On the other hand, as Kant said one time, it seems as if in describing something as X, I do not (qualitatively) describe less of it than when I describe it as an existent X. So the naively free-floating use of the word "exists" is ambiguated between inherently uninformative meanings.⚝ (Note: this does not mean that quantifiers are useless, just that their usefulness is independent on whether they are taken to recapitulate our ontological naivete.) In a slogan, "Nothing exists." The slogan explained: not, then, however, to say that things do the opposite of existing, either; or, just because something doesn't exist, doesn't mean that true statements about it cannot be made. The modern princess of Antarctica has not shaved her head, for instance, but she also has no head to shave and isn't actually a princess, for that matter, either.
Atheism. It would be pointless to say, "God does not exist," then. Of course It doesn't exist: nothing whatsoever exists! But it would not be pointless to say, "God did not create the world." That is what an atheist would say in this context; that or, then, "The world was not created by God."
What would justify an atheist in saying this, though? Now, there are many uses of the word "creation," and some are allowable, here, e.g., "Matter was rearranged into the form of X," is the from-prior-substance definition, and to reword that as, "X was created," would go through as such. But the general definition of "creation" is "to cause to exist," which then adverts to either the naive use of the word "existence" that was presuppositionally ruled out, or to sophisticated replacement assertions. It seems as though talk of "creation from nothingness" involves ontological naivete, as if nothingness too is a real predicate alongside somethingness, which after all we just said that we deny, here.
In other words: is saying, "God created the world from nothingness," the same as saying, "God predicated existence of the world"? Yet then if existence is not a predicate, or if it is pointless to talk about things existing as such, then our atheism would be stated as, "The world was not caused to exist from nothing," and even, "God did not create the world from nothing." But it seems strange to be able to deduce atheism, even in this form, from abstract premises.
⚝Consider the peculiarity of asking, "Why is there something instead of nothing?" This doesn't seem so far from asking, "Why are there reasons-why for anything?" or anyway, the answer to the former would seem as if it would have to involve the answer to the latter. But if the latter is pointless, so too is the former; or, again, asking about things existing in such a free-floating way seems like not asking a real question.