What can suffice as a scientific proof for God:
Before you know how someone can prove a concept like a God you need a proper description of a God's nature. If a God is something beyond proper description with any of the concepts or properties that we can employ, a being that defies comprehension, it cannot be clear to even the believer what he believes, or whether his pious belief has any content at all. There has been no unanimity in human conceptions of the divine. There is little evidence of common consent here. On what possible grounds can it be asserted that these seemingly radically different concepts are, at bottom, the same concept? If there is a same concept, what it would take for an idea of the divine not to share in that same concept?
To a proof to be a scientific proof of a God it must cohere with our other beliefs, the scientific theories. It would be necessary that a God hypothesis would not be superfluous to explain and understand better the workings the world we observe. The God hypothesis may be challenged if it make no contribution to the predictive success of actual science.The history of science gives us reasons to be wary of committing ourselves to the existence of the unobservables postulated to explain observable phenomena. Since there are many ontologically incompatible yet empirically equivalent Gods, some ‘principle of privilege’ is required if we are to think that a God that we can have under consideration is the true God. How we can know that none of the other possible God's we have not considered until now is not better than the best that we have now? Obsolete Gods, which no longer have active adherents, are evidence that holy books are not so eternal.
Is the God you want to prove a necessary God? Of all possible proves, a deduction is the strategy that we would expect to be successful were there a necessary God. As there isn't a valid deduction of any non logical existence, we can conclude that there is no necessary God.
What domain can such a proof belong to?
The absence of evidence is not the evidence of absence, but what can be asserted without proof can be dismissed without proof. Extraordinary claims require extraordinary evidence. The burden of proof lies upon a person making scientifically untestable claims. My or your inability to invalidate the existence of Zeus or an Hindu God or your imagination, is not at all the same thing as proving it true.
We do not have a priori disproof that many things do not exist, yet it is reasonable and justified to believe that they do not: flying pink unicorns are not real, there is no Santa Claus, a defendant is not guilty, a patient does not have a particular disease, so on. None of these achieve the level of deductive proof. Believing that something does not exist is reasonable even though no logical impossibility is manifest. Believing that something exist or even being agnostic about their existence on the basis of their mere possibility would not be justified.
Believers in a God don't want treating the hypothesis of a God as just one more scientific hypothesis, to be evaluated by the standards of science in particular and rational thought in general, their faith is quite beyond reason, not a matter to which such mundane methods of testing applies. But there is no evidence that a religious faith that rejects reason would also serve us while seeking truth. If faith is the only way to know the truth of a God, how are we to know which God to have faith in?
Atheists just believe in one fewer god than the monotheistic believers. When monotheistic believers understand why they refuse all the other possible gods, they will understand why atheists reject the myth of them too. A religion rejects other religions precisely because they are faith-based, there is no evidence for them. One can't prove that a God doesn't exist, but science makes a God unnecessary.