This cannot be determined with certainty because each individual will have differing criteria and degrees of certitude in weighing any kind of evidence, scientific or otherwise, about the matter. Whether God is real or not will always be in the mind of the beholder. To be sure, there are fantastic miracles we could conjure up that would persuade almost anyone of sound mind that we are indeed the Almighty, but we are simply staying within the limits of our own rules in setting this experiment in motion, which is the Human Experiment, to give you sovereignty over your own lives and your world so you are in charge and not us. For that to be meaningful, we must stay behind the scenes, available to you but not controlling things directly or altering what you might do, or not do, unilaterally, even if we can see it would be helpful in some way and even prevent a disaster. What you are experiencing is real, that you are on your own, and everything matters, everything counts.
So using science to try to probe observable reality is all well and good, but it is a kind of circular argument in the sense that observations will lead to new hypotheses, and that will lead to making new observations that will lead to further hypotheses. Who is to say when you have arrived at the goal of obtaining proof? Many would say the existence of the natural beauty around you and the existence of life itself, especially in the advanced form that constitutes a human being, is indeed a wondrous miracle that is impossible to have happened through chance events alone. Yet science makes the opposite argument that simply ignores the wonderment and awe of someone seeing the reality of how truly complicated, intricate, and purposeful everything about life forms turns out to be. Going in with science and dissecting things, down to the molecular and even submolecular level, has been rewarding to human curiosity, but at some point there must be an openness to the truth of things in order for the mind to accept the leap of faith required to draw conclusions about God from what is observed through the ordinary senses.
So we would say that this is a typical thought experiment a scientist would come up with, assuming that it is indeed science that can address the issue and will be the ultimate tool for carrying out an investigation to arrive at the truth of things. When this is entirely a conjecture based on an assumption with no underpinnings, it is floating on a sea of ignorance, and that is the folly in the proposal, that it is based on the ignorance of the scientist to make the assumptions that perhaps science can take us to God. So the question has within it the built-in bias of the scientist who thinks of science as the answer because science is what that individual prizes and believes in.
Our perspective about science is that what scientists see and accept, based on their very simplistic and superficial explorations, is hardly the be-all and end-all of knowledge. What is needed to address the question is an ability to have an open mind and to think beyond what is tangible and observable through the ordinary senses. That is the only way you will reach a God that is behind the scenes when your natural bias, having grown up on your planet surrounded by the bounties of nature and the wondrousness of everything in physical creation, takes it all for granted. So again, one is left with bias, and round and round you go in any way you might choose to find a path to God. As we said at the outset, any evidence you acquire will be subjective and you will not have unanimity of agreement, and hence it will be not proof, but opinion in the end.
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