God and Science really have nothing to do with your question, premise or argument. The issue is a combination of semantics and philosophy.

"God" is indeed what we can't explain (among other things we can't explain). Nobody can "explain" "God" and nobody ever will. So the question "does God exist?" is a meaningless question.

Science is all about explanation. But Science cannot explain everything. Every explanation triggers a new question, like in cosmology and quantum mechanics. So it's foolish waiting for Science to explain all mysteries, even though it continues to make progress.

Human beings have limited intellectual grasp. If God "exists" then God is outside our intellectual grasp. We can't talk meaningfully about what's outside our intellectual grasp. If God exists, then God is beyond our understanding.

So let's stop banging our heads against the wall trying to resolve such questions. For us humans, there are no answers -- no answers one way, or the other.

As Wittgenstein said "what we cannot speak about, let us pass over in silence."