Stolen from Carl Sagan, emphasis mine.
"A fire-breathing dragon lives in my garage."
Suppose I seriously make such an assertion to you. Surely you’d want to check it out, see for yourself. There have been innumerable stories of dragons over the centuries, but no real evidence. What an opportunity!
"Show me," you say. I lead you to my garage. You look inside and see a ladder, some empty paint cans, an old tricycle – but no dragon.
"Where’s the dragon?" you ask.
"Oh, she’s right here," I reply, waving vaguely. "I neglected to mention that she’s an invisible dragon."
You propose spreading flour on the floor of the garage to capture the dragon’s footprints.
"Good idea," I say, "but this dragon floats in the air."
Then you’ll use an infrared sensor to detect the invisible fire.
"Good idea, but the invisible fire is also heatless."
You’ll spray paint the dragon to make her visible.
"Good idea, except she’s an incorporeal dragon and the paint won’t stick."
And so on. I counter every physical test you propose with a special explanation of why it won’t work.
Now, what’s the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all? If there’s no way to disprove my contention, no conceivable experiment that would count against it, what does it mean to say that my dragon exists? Claims that cannot be tested, assertions immune to disproof are veridically worthless, whatever value they may have in inspiring our sense of wonder. What I’m asking you to do comes down to believing, in the absence of evidence, on my say-so.
Sorry Beowulf, but your logic is bass-ackwards. Just like this dragon here, you can't prove God exists without some evidence to indicate its existence.