If the skies errupted with the sound of trumpets and an angel descended to tell me to do something, my first thought would probably be that I'm having some sort of mental break, but if the person standing next me is seeing it, too, then I'll be the first one carving some commandments or whatever. There's a perfectly achievable standard of proof for you.
Defining God as supernatural and unprovable would lead the absurd situation that if God made Themselves self-evidently provable to everyone (say, with the whole trumpets and angels routine), then the alleged faithful would reject Him for not being their God, while He would only be believed by nonbelievers.
Sure, an Angel descending from the heavens would shatter our existing scientific understanding of the world, but that wouldn't make it intrinsically supernatural. It just would reveal a whole branch of knowledge that we didn't previously have any lines of inquiry into.
