Seriously?
Ok, here it goes...
At some point in my past - decades ago now - something extraordinary happened to me. Something that I could not explain then, even though I tried hard to unravel this mystery. Something that has bothered me for the rest of my life. The sole time that I might say that something "supernatural" happened to me... though there still are a few potential natural explanations, that I simply do not any means to test for, then and now.
Reaching "out" for an answer is something that I cannot do... I could never be certain that I didn't simply imagine it, even if I were to "find" any answer at all.
So what I want you to do is: pray!
Don't pray that this extraordinary event is explained to me... but that God shows this to you, and then relate this revelation to me.
Ask him to reveal to you to circumstance of what happened - that is my safeguard to know that it isn't you who is imagining things - and what the explanation behind this event was.
If you can do that, I will accept that as evidence for the existence and power of God.
This isn't asking for a circus trick or something that will grant me any personal gain (except for some peace of mind). I am not asking for the number I am just now thinking of, or next weeks lottery results. This is a serious request.
There are two options here...one is that it happens and you simply say it is incorrect! The second is that others HAVE had the exact same experience (or something alarmingly similar) and because you will not reveal it, no one can know (including yourself).
The error in this scenario is you are requiring
I prove to you this apparently outside "the natural order" experience happened to you, where only you know it either did or did not actually happen (we do not know, though I would believe it could have because of my own such experiences when I was an agnostic). I will say however that having had a number of such experiences WERE part of what led ME to seriously consider the reality of a God(s) (which I formerly believed to be either a lie, a delusion, superstition, or brainwashing).
This is not a gift I possess, but my not having it does not prove there is not a God or super intelligence at work on the Universe. Now should I pray and receive a possible answer to that prayer being outside the "natural order" (as you would define natural) there would be no material test to prove it and we are back to the "two options" mentioned earlier.
All I can say is that
IF such a thing has actually happened to YOU,
THEN myself having had a few such experiences (though I would not say they were of God) I would say this is for you to decide what to do with it, for I KNOW that even if I were able to satisfy this request you would still find it inadequate to believe this demonstrated there is a God (and I know this from personal experience).
I could ask you to do the exact same thing which YOU also would not be able to do, and that is not "evidence" for OR against the possibility that there is or is not a God just that there is or is not "outside of the Natural order" phenomena or experiences (many of which may one day be proven to be quite natural)! For example, many centuries ago, people believed invisible life forms were responsible for many diseases.
They believed these invisible life forms would possess/invade/take over the body and cause all sorts of havoc in the body and mind (even kill). They called them spirits...of course NOW we know they were correct after all only we call them bacteria and virus's and now have extended our ability to see them through intelligently designed instrumentation.