Much of science is inference of stuff you can not see or test directly. We infer from observations, for example using probability analysis. You have a "belief" that G-d is impossible to even logically infer from observation. That belief has NO support.
But when you don't understand what you are talking about, your "indirect" testing is worthless. And when there is a non-zero chance of something naturally occurring, that result does not require a supernatural explanation, by definition.
But what I find interesting is that you can not only "infer" the existence of this God, but his identity as well. Or else why the coy "G-d" stuff. Does Hercules care if you deface his name? Would Shiva give a damn if his name were erased? Or is it only Yahweh who can make a coin land on heads fifty times. So, you clearly believe that you know about not only God's existence, but his nature, as well. Tell me, exactly what is the scientific basis for your ideas about the nature and identity of God?
You have a "belief" that G-d is impossible to even logically infer from observation. That belief has NO support.
I believe that you cannot prove God's existence. You can infer whatever you want. That doesn't necessarily mean that it is correct, though.