God is on Earth and is trying to convince someone without using any power.
A power is anything that no human can do.
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Pretty tricky to do really. In fact, I don't believe it's possible.
You may be able to empirically test that its construction is not biologically possible (or, perhaps, biological at all). Presumably a being capable of the miracles of God would have a physical form that defies known physics. This is not a 'power' of God as it is simply a fundamental of its existence.
This lends weight to its assertions that it is God, but is not in itself proof. It could also be true that it is a sufficiently advanced alien and/or that our understanding of physics is not yet complete.
In fact, demonstration of Godly power would likewise be explainable via Clarke's Third Law (or, rather, Sherman's Law). Proving something is God is tricky even without restrictions.
For reference Sherman's Law is: 'Any sufficiently advanced alien is indistinguishable from god.'
Looks and following.
A heavenly host of mal'āk̠ 'ĕlōhîm would throng around praising a Hebrew God.
Angels and Archangels the same with a Christian one.
Malak to an Islamic one.
... and so on with Zoroastrianism, Sikhism etc.
Other gods are more conspicuous by their very nature.
When having a weekend in the Lake district Godspotting, it's important to bring your field guide to god identification. Watch out for the occasional rare specimens.
Shiva - three eyes, four arms, covered in ash etc..
Ganesha - very well dressed, talking, elephant.
Thor - big hammer, big muscles, slow wit, quick to anger if you point that out to him. Speaks archaic Norse.
Proteus - in natural form (not using protean powers) has a fish tail.
It really only takes the power of persuasion. Many religions have been founded simply by a person being able to persuade others that he or she is the Annointed, the Deity Incarnate or even the Second Coming of Christ. This is especially true of cult religions which are multitudinous and various.
One aspect of the being attempting to demonstrate its deityhood without actually doing anything is its appearance. The OP's question doesn't give any clues to this aspect. Appearance alone might be sufficient for people to believe they have encountered a god.
This might come to something as simple as wearing a name tag with the label "I AM GOD".
Although descending from the Heavens on a beam of light might be dead giveaway.
What's the difference between the incarnate God, and a human? The only difference is, that the God can do stuff that a human can't. What he does is up to him, it can be stark miracles like fire falling from heaven, or subtle ones like precise knowledge of a person's past without ever having met him/her before. But it must be something that a human cannot do. Because otherwise, Occam's razor tells us to assume he's just a human. As such, God cannot prove himself without demonstrating supernatural powers.
Btw, that's precisely why Christians think that the miracles that Jesus did are so important: No miracles => zero indication that Jesus is indeed God. However, if it's true that Jesus did walk on water, or rose from the dead, well, then God must be involved.