You have that a little wrong. God *can* (in principle) be proven. If the sky breaks open, choirs of angels break forth, a 10km-long arm reaches down from the skies and an 8km golden-haired, bearded face looks down upon humanity and utters words of unshakable truth...then God is proven.
That ostentatious display of fireworks wouldn't prove that the entity responsible for them would be omniscient, all-powerful, omnipresent and all-benevolent, though.
These are characteristics that those in the know consider essential properties of what they call "God", and those wouldn't be proven by your hypothetical display of evidence; that would only show that someone has a tremendous FX budget.
By their very definition, those "omni" properties cannot be proven by empirical evidence, so by definition they are outside the reach of scientific enquiry, and belong to the realm of the purely philosophical. All theology and most classic philosophy depend on those universal, unlimited powers of God for their reasoning, so most of what you've heard about such entity would still remain unproven. That's why all this talk about "science can prove the existence of God" or "science can prove that God doesn't exist" is quite silly; they would anyway work only for some trivial values of God, not its core definition.