As noted, this position does not negate the existence of GOD, and in any case does not clash head-on with theism. Theism makes an ontological claim: there is a GOD. This kind of atheism makes an epistemological claim: there is no proof of the existence of GOD. There is no contradiction between the two claims.
One can believe that GOD exists and at the same time agree that there is no way to prove it. There are many ideas or closely held beliefs that cannot be proved, and yet they may exist, e.g., extraterrestrial beings. Nor is it possible to prove whether a redheaded man named Fred lived in England 4,000 years ago, and yet it is quite possible that such a man existed. The question is, what to do with a lack of evidence to prove the existence or not of any belief? Does a rational person justify a decisive apostasy in the existence of the object sought, or is the rational choice to remain in doubt about any considered belief?
This is already a question of an “a priori” premise, how plausible the existence of the same object seems to be. If that object seems a priori to be manifestly unreasonable, then the lack of evidence for its existence justifies the conclusion that it probably does not exist.
But if the premise is that the existence of the same object is a reasonable idea, then this lack of evidence should not cause one to deny its existence, or at least the possibility of its existence.
So it is with aliens, Fred the redhead, and understandably it is also so with the idea of the existence of GOD. There will be more discussion on this line of reasoning in the next section on this topic.