But you can prove what the explanation wouldn't be, what it wouldn't involve. It would not involve logical contradictions, primarily. So an illogical God creating the universe can be disproven, i.e. that aspect of him can be refuted.
I agree. Anything that introduces contradictions can be ruled out, so it is essentially a negative filter on candidate explanations.
However, it only tells us what the explanation
cannot be. It doesn't give us a positive reason to posit God in the first place, nor does it make the remaining God claim any less placeholder-like. That is, filtering does not supply evidence or establish a connection to reality.
God normally consists of metaphysical claims that involve, for one, how the universe came to exist.
Even then, this boils down to one of two broad cases.
One is
What I would refer to as "God", I would refer to the initial conditions of creating the Big Bang.
in which "God" effectively becomes a label for underlying physical conditions or laws. Which is a perfectly legitimate area of inquiry, but then the label "God" isn't really adding anything beyond what physics is already trying to describe. It's just an extra label for unknown natural conditions and in that sense it doesn't contribute additional explanatory value.
The other option is to treat "God" as some kind of causal agent behind those conditions.
At that point, unless that claim places constraints on what we should expect to observe (or on how reality would differ depending on whether that agent is involved) it doesn't function as an explanation. Like, a good explanation usually narrows things down, it tells us "if this is true, then we should expect xyz rather than abc". Without that kind of constraint, the idea doesn't guide our understanding or help us distinguish between possibilities, it just adds another layer.
More than that, it expands the set of open questions. Once an agent is introduced, you now have to account for questions like what kind of agent it is, how it brings about effects, why it has those features rather than others, and how it relates to the regularities we already observe. For instance, if we're trying to explain why the universe has the structure it does, we now also have to ask why this agent is able to produce exactly that structure, and not something else. So, not only do the original questions remain, an additional set gets introduced. The underlying phenomena still require explanation, and now the agent itself does as well.