This is a tricky one, isn't it? If we could show the existence of God by measuring "divine influence" or "divine presence" by some kind of theometer, we'd have proved that He/She was part of the material world... and therefore not divine by most people's definition.
I'm reminded of Douglas Adam's argument that a real, incontrovertible miracle would be final proof of the non-existence of God:
"I refuse to prove I exist," says God, "because proof denies faith and without faith I am nothing."
"Ah," says Man, "but the Babel Fish is a dead giveaway. It proves you exist, therefore you don't. QED."
"Oh, I hadn't thought of that," says God, and vanishes in a puff of logic.
"Oh, that was easy," says Man, and for an encore proves that black is white and is run over on a zebra crossing.
(The Hitchhiker's Guide to the Galaxy)
But seriously, it's hard to think of any manifestation that wouldn't reduce the divinity to a science-fiction super-being on the lines of Galactus. I guess that's why I'm happier to know my Goddess in my heart, but not expect Her to leave footprints in the material world.