Asking if it’s possible there are gods … obviously, there’s going to be a problem with language here, such as with “exist” and “possible” and so on. “Possible” cannot be akin here to “probable” (Ayer, “Language Truth and Logic”) and “exist” generally put as “manifest in reality”.
So in saying God is possible, we can only mean “logically possible” and to “exist”, I’m not sure we know exactly what we mean other than a “super” natural “reality” (Smith, “Atheism: The Case Against God”) which places God outside of our comprehension but leaves us at least with the idea that whatever that reality is, God is present and known.
In asking the question “Does God exist?”, we can only be saying there is an ineffable reality unknown to us and we’re imagining what the real implications are for us; “real” being about our comprehended world.
The existence of God as the end of our concern can’t possibly matter. The question is a means to an end and that end is found in the questions “Why anything at all?”, “Why this place?” and “Why a place like this?”. If we then take our thoughts on God’s possible existence, the only reason and way they could find meaning is that they somehow apply to these questions.
While I find the question of God’s existence in all ways pointless in itself, should I have an impression of some “Big Other”, what I make of it may matter quit a lot.
The difficulty is that we can take nearly any general absurdity and make coherent statements, and we understand already that logic is in the end, a formalized language descriptive of how folks think, that it proves nothing in actuality, and rational god-talk in terms of moving us in any direction nearer or farther from believing “There are gods” is fairly impotent. One would have to ask about a functional benefit to any single sentence or volume of them that are descriptive of “the present King of France” (Russell, “On Denoting”). And where this leaves the apologist with such proofs of God, presenting them to non believers, is at a loss. The failure there is not understanding that without some real and relatable experience, both God and “the present King of France” are equal and worth the same, which is to say they’re both worthless. These are happy to let the believer find value in these thought-games, but they find none in it themselves; only becoming interested when believers foist their musings onto society as a whole and those musings are negatives within it.
So the only question left seems to be perhaps in asking what way it matters to anyone whether or not there are gods.