Recently, I was reading a very reasonable and well thought out debate on proof that God exists and whether or not there is such proof or if it is even possible to prove that God exists. For me, the main problem with questions of "proof" of any concept is that there is an assumption that humans are equipped to experience any given entity or material and their inability to experience it means it does not exist. In particular, if we can't see, smell, feel, hear, or taste it or invent a mechanism that can translate a phenomenon into data which we can apply one of those senses to, we say it cannot be proven. This is the unavoidable flaw when science tries to "prove" metaphysical concepts. It is limited to what our meat sacks can comprehend, and we're hardly the best instruments. If "God" is out there, we may be no more capable of comprehending it than a tree is capable of having a conversation with us.
The other problem is that people are constantly framing "God" concepts in their own image, and I don't just mean the psychological concepts like judging people or issuing rules to run their lives. There may indeed be some sort of greater entity that set the universe in motion and is monitoring every action that goes on, but that doesn't mean it is paternalistic or concerns itself with what goes on in our lives beyond some sort of perception that changes of some sort are occurring. Whatever "God" is does not have to be some single entity looking after our welfare. It could simply be something that spawns energy or reorganizes it or has some sort of imperative to see matter and energy manipulated into different patterns or frequencies. If that is so, it doesn't mean that that entity has no interest in our improving ourselves or our world, but rather that our achievements mentally, emotionally, or spiritually bring about that entity's desired changes to energy or matter.
We can't prove it, but I think there is far less value in proof than in thinking more expansively about the concepts and what they mean to our lives than in seeking proof. If there is any "proof" to be had, it won't come as a result of prognostication and fulfillment of a prediction, scientific research, or personal experience. It'll come from an analysis of trends and looking for a certain pattern of interaction both in the way civilizations and people change across thousands of years and by studying the interaction of matter and energy on an atomic level.