It is quite possible to prove
How?
You've already given the answer yourself! Satoshi has mined the first bitcoin block which we also call as genesis block. If real Satoshi wants to identify himself, he can simply use his key to sign a message! That's it!
Unless and until the key is hacked by a hacker (which is highly unlikely), there's no way to impersonate!
What do you think can be a irrefutable proof other than this?