Wow, that is … a very difficult question.
I think this question might actually be a good example of why the concept of an omnipotent being is logically incoherent. It’s sort of a variation on the old, “Could God make a boulder so heavy he couldn’t move it?” question. Presumably, an omnipotent being would have some way of conclusively demonstrating His omnipotence, but the manner in which He would do so eludes me.
Certainly, none of the miracles in the Bible could, in isolation, be taken as proof of omnipotence. As the Oxford logic professor Alfred Ayer points out in Language, Truth and Logic, verifiable phenomena demonstrate only themselves, and not any metaphysical properties you might want to associate with them. So, for example, if we had definitive proof that the Biblical parting of the Red Sea did, in fact, occur, and that there was no other readily available naturalistic explanation for that phenomenon, you might be tempted to say that it was a miracle and proved the existence of God. But all that it really proves is that there exists something we don’t yet understand which caused something else to happen. If the word “God” is exhausted by the definition “that which parted the Red Sea,” then yes, its existence is undeniable. But it doesn’t follow that this entity is omnipotent, or even sentient.
So perhaps the only way to directly experience the existence of an omnipotent God is to be that God.