You don't have to be able to see something to know it exists. You can't see oxygen, but just try living without it. The atom has been proven to exist, through many detailed, and repeatable, scientific experiments. We know from experimentation that, if you combine certain atoms under certain conditions you will get the same result every time.
I've heard people who claim that something which seemed miraculous to them proves the existence of God. For example, someone surviving an accident which, by all rights, should have killed them. But there are far too many accidents in which someone who should have survived doesn't. Why didn't God intervene there?
I've heard people who claim that God must have created the world because it's just too complex to have developed on its own. Yet when confronted with the all too frequent breakdowns of those complex systems, something an infallible God should have been able to avoid, they place the blame on Satan. Why is it that anything bad that happens has to be Satan's fault, and not God's?
No, I'm afraid that we can never prove that God exists until the time that he stands in front of the world and proves beyond any shadow of a doubt that he does. But by the same token, we can never prove that he does not exist, either. It is, and always will be, a matter of faith.