Before giving anything like a full answer to this question I would have to know what you mean by "God" - i.e. I would have to know what I would supposedly be looking for evidence about.
However, there is an exaple that was discussed here some time ago. We looked at what evidence we would need to consider "fulfilled prophecy" as significant evidence of God. We came up with some pretty good criteria for what would be accepted. But we weren't offered any real examples or any decent rebuttals to the criteria.
This is a relevant thread, although there are many others discussing prophecy. The first post is the really important one from my point of view (although there are some refinements to be made)
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