Can't prove the supernatural God

[SteveII]

I will say that it is very reasonable to look for a natural explanation before positing a miracle happened since our experience does support that that is the case in almost all events.

All events. Our experience supports that in ALL events. Of the known explanations and causes for things, we have natural things, and we have unknowns. There are absolutely zero known, demonstrable supernatural causes, effects, or objects.

Aside from that caveat, I appreciate the concession. I am still a little unclear, however, on how you're distinguishing a regular unlikely event from a miracle. If the person happens to have prayed for it first, how do you rule out coincidence (and how do you explain the fact that prayers, regardless of the religion, have zero demonstrable effect on any outcome when compared with pure chance?)? If the person came to god or experienced personal growth from it, how do you explain when that same thing happens, but with somebody else's god? If an unexplained tumor-remission brings someone closer to Thor, is that evidence that Thor exists? If not, why should it be evidence that Jesus exists?

Your first paragraph relies on dismissing the entire NT (and any other claims of miracles). But in addition, even though you are carefully wording your sentence, you are really saying that events can only have naturalistic explanations. You are simply moving "unknowns" over to the naturalistic column for no reason other than they must not have had a supernatural cause. Why is this not the equivalent of saying " miracles do not exist because miracle can't happen"--which is circular?
I do keep hearing the claim that healing happens at the same rate between religious and non-religious. Do you have something that explains that study? Please note, I was not using modern healing miracles as evidence in this discussion because of some of the reasons you pointed out.