When science finds a proposed mechanism for what used to be a gap, that does not mean that it is evidence that God does not exist.
No discovery of science can disprove the existence of a god, but if science shows us that the world works automatically without intelligent supervision, then the question of whether a god set it all in action becomes irrelevant and any such god becomes irrelevant. It's also an unanswerable question.
Science cannot prove a negative, that things were not designed, even if a potential "natural" mechanism is found for all processes.
Science cannot prove that there is a designer even if it seems that there is no way for something to have happened "naturally".
What you are saying is that the god to which you refer is undetectable by any means at any time or place, which means that it has no discernible impact on reality, and once again, the question of its existence becomes irrelevant. It also makes it indistinguishable from a fictional character, which also cannot affect reality. The ideas that such things exist can affect individual realities, but if their referents don't exist or don't impact existence, they are indistinguishable from the nonexistent and can be treated as nonexistent.
When you say "Science is the study of reality", that is just a claim of faith.
I disagree. That's a description of what science does. You want to cling onto concepts like gods, a spiritual realm, and supernaturalism. You want to call them real but beyond science's purview, and you can, but empiricists are free to disregard all such claims. Their attention is on what IS discernible, not what cannot be detected.
Why don't you demonstrate that it is possible that there is no designer?
Besides being impossible, it would be a useless demonstration to an empiricist, who already has no designer in his worldview.
"Natural process" does not actually mean that God has had nothing to do with the creation of the process.
It means that the process runs itself automatically. If a god were once involved in that, it's not now. The god you describe actually does nothing anymore and is needed for nothing if nature can unfold according to ancient principles that act automatically.