The question of "god or advanced alien" has been the premise of quite a few Star Trek episodes. When it comes down to it, it's just a question of labeling, which is not terribly important. In the original series episode "Who Mourns for Adonis," the Enterprise encounters a being representing himself as the Greek god Apollo. The entity uses impressive powers to try to convince Kirk and the others to worship him and return to a primitive, pastoral existence. Kirk never spends too much time with arguments about whether he really is "the" Apollo the ancient Greeks worshiped or not, and whether he's a "god" or an "alien." His response is basically, "We've outgrown you. Oh, and we have phasers."
So, if a believer wants to prove their god or goddess exists, they do it the same way we prove anything else (e.g. a "Higgs Boson") exists: get it to show up. Or to be more precise, devise some kind of test, specifying anticipated consequences that would result if the entity exists, vs. anticipated consequences that would result if it does not, so that both sides can agree which results reflect which outcome, and no fudging afterward. If an entity shows up claiming to be the Christian deity, speaking through pillars of cloud and fire in a thunderous voice, conferring powers upon its followers per The Wannabe's post, and causing effects ("miracles") like those found in the Bible, then we might as well go ahead and call it "Yahweh" or "Jesus" while lining it up in our targeting reticules. We would still have good reason to doubt that it is "the actual god of the Bible" because of the absence of physical and historical evidence for the divine feats described therein (e.g., the Exodus, the darkness and earthquake and zombie invasion at the time of Jesus' death, etc.). But, if it has the power to rain fire and brimstone down on our cities and somehow cage us in a realm of endless maximal torment, it doesn't really matter for practical intents and purposes whether it's doing so by "miraculous power" or "proton-beams and uploading of human consciousnesses into a Hellish computer simulation." Our array of available responses (fight, surrender, negotiate, try to buy time, etc.) would be the same.
Let's consider a "miracle," say, Jesus feeding the 5,000 with three loaves and two fishes. Question for the believer: assuming this happened, was there some way in which it actually
worked? It may be beyond our comprehension, sure, but what about
Jesus'? Does
he know how the process worked? Would he be able to explain it as, say, a transformation of theon particle/wave/23-dimensional hypertoroid spacetime manifold loops/whatever into ordinary matter configured into the form of bread and fish by means of [insert 10,000 pages of super-scary equations here]? If there was any sort of "actual way it worked," no matter how far beyond human ken it might be...
Congratulations! It's a natural event! Why? Because the process, whatever it was, occurred in accordance with the
natures of the entities and forces involved (Jesus, theon particles, fish and bread, and any other relevant entities or forces). All kinds of things that were once considered "supernatural" (storms, disease, fertility, infertility, probability aka "luck," the Sun, etc., etc.) are now considered "natural" because we figured out how they work. Since "humans know how it works" is not an ontological property of things in themselves (so that the Sun actually changed from a supernatural to a natural entity once we discovered that it works by means of nuclear fusion), the term "supernatural" is basically emptied of content.
The best counter I've seen so far to this argument is Richard Carrier's attempt to define "supernatural" as a reference to ontologically mental things. That is, "supernatural" refers to things like cognition, emotion, thoughts, will, minds, etc. existing wholly independent of any brain or comparable mass-energy substrate (like a computer, interference pattern of standing waves, configuration of warped spacetime, whatever). I doubt that this is a coherent concept. If you have a deity that is "ontologically mental" in this way, then the question arises: is there a "way it actually works" (no matter how complex or beyond human comprehension it might be), or not? If there is, then "ontologically mental things" still have an
explanation, even if human minds are too feeble to understand it. The "ontologically mental" becomes explicable/reducible in terms of "spirit energy" or some such, which we can then add to our inventory of known natural forces/entities. If there is no "way it actually works," then we're talking about something that works without a way to work, which is (I think) a logical contradiction. How could a deity be "Yahweh" (and not "Odin" or "Isis") without having a
nature that makes him work in a particular way so as to constitute "Yahweh?"
So, it seems rather difficult for a deity or other supposedly "supernatural" entity that actually exists to avoid turning out to be a natural entity after all; in which case the distinction between "god" and "alien" is just a matter of preference in labeling.
The one remaining escape route from this conundrum is the claim by the Abrahamic monotheisms that a "true" God must, by definition, be an omnimax (e.g. Anselm's Ontological Argument). In this case, the difficulty in proving that a given god is "omnipotent" rather than just really, really,
really powerful is a problem caused by the incoherence of the term "omnipotent" rather than a flaw in the epistemology of critical thinking, testing, and validation (or "proof") of ideas. Since the concept of "omnipotence" is incoherent, incompatible with the Biblical narratives about Yahweh (e.g. Judges 1:19, etc.), and logically contradictory to the other omni-attributes
[1] we have full logical warrant to reject it (and the other omni-attributes) as potential properties of a deity.
So that leaves us, again, with natural deities/aliens. Proof of their existence requires only that they show up, just like any other real thing or force.
