Hmm, well proof for or against the existence of a God would be rather impossible I'd think. But one could infer that existence or non-existence based on clues in the natural world.
For myself, I consider the origin of life (evolution, etc) and the origin of the universe (big bang, etc) to, if not be correct theories, at least mostly correct. I only say that because the more we learn, the more our theories seem to require a little fine tuning.
What bothers me, specifically, is life itself, or the existence thereof and the observed path of evolution. I mean, Darwinian evolution is all well and good, but much of observed evolution (such as the leap in size of the human brain from our primate ancestors) doesn't make a lot of evolutionary sense. Why does any creature require such a complex brain? It serves no purpose from an evolutionary point of view, it is just a rather convenient thing we humans have that sets us completely apart from the rest of life on Earth.
Another thing that I have a hang up about with life is DNA. Sure, I have seen the arguments between die-hard atheists and religious people, but never is the question quite answered as such discussions either devolve into name calling or go off on tangents...where does DNA come from? How could something that is a lot like a complex computer code come from a mixed bag of proteins? Sheer chance or random happenstance? I think that is an extraordinary claim, which of course, as we all like to quote, requires extraordinary evidence. Of course, such a thing could happen I suppose, I just have a hard time believing it.
And evolution itself. Driven by natural selection and random genetic mutation (or genetic "drift" if you like). Natural selection is a process that is observable and quite well understood. It makes complete sense. When it comes to the other component, genetic mutation, that is questionable. Yes, mutations would have to occur. But are they random? We can observe random mutations. Many experiments have been done to see what mutations can occur and what their effect on an organism will be. And, as far as I know, they have all been either disastrous to the organism or had no effect. I could be wrong, but I have yet to read anything about such experiments producing an organism that is in some way improved or at least affected positively from a random mutation to its DNA. Microorganisms are probably the best sample we have since their life-cycles are so fast compared to other organisms. And we do see that they mutate in nature, as there is a different strain of bacteria or a virus that resists treatments or becomes infectious to organisms it didn't infect before. But is this driven by random mutation, or is there an aspect of its DNA at work that intelligently chooses mutations to benefit itself?
So I question whether DNA isn't a bit more complex than we currently perceive. Perhaps it has the ability to not only drive its own evolution, but maybe to prevent or repair "bad mutations". And if this is the case, then it leads back to my original question of, where did such a complex thing, the basis of all life, come from? Mere happenstance? Extraordinary claim I think.
I could even argue about the universe itself. Why is our universe so filled with matter? Why not anti-matter? Why wasn't there an equal number of matter and anti-matter formed when the universe cooled, and then annihilated? Granted, most matter must have been annihilated in those early moments of the universe, leaving a very small amount of matter behind...but that means there was more matter than antimatter, which doesn't seem to follow theory, unless I misunderstand such theory of matter and energy.
Sure, none of this "proves" there is some creator or some such, but it does rather make it hard to definitively say "there is no God", or to even act as if such a notion is crazy, when it is no more preposterous, in my mind, than DNA popping out of nowhere. Sure, there could be a God, and sure DNA could have popped out of nowhere. Maybe science will answer this dilemma some day, but then maybe not.
As for the super natural, I look at it this way. By definition, something that is "super natural" is outside of nature. If nature is a system, then super nature is a separate system "above" or "outside" if nature. Nature, being the system we see, experience, are a part of, and can interact with. I would assume also, that nature, or a natural system, would be defined by its own set of physical laws and characteristics. Which would mean, by definition, that a separate system, a "super nature" would also have its own set of laws. And in that regard, I think it would be difficult, if not impossible, to scientifically prove anything about another natural system from the perspective of our natural system.