While I respect and applaud the OP's author for 'thinking outside the box', so to speak, in trying to find a poignant comparison to God that employs a particular 'myth' or 'legend' simulataneously existing in numerous cultures, many of which have apparently had no substantive contact with one another, thereby seeming to eliminate some sort of cultural-mythological domino effect in which one group of people conceived the idea of 'dragons' and passed them on to others, I still find one irreconcilable fault with the analogy/question.
Some 'theists' believe that our existence, the very existence of the universe itself, is evidence of God. Now, don't get me wrong, I am not saying I agree with this notion. But I could certainly see how it would be possible for some theists to be dismissive of the OP's question because Dragons, even if they do exist or ever did, have left nothing that can be referred to as 'evidence' of that existence.
Some theists claim the very fact that a material universe exists, one for which there is NO verifiably known origin, at least none we have yet found, that alone is indication/evidence of God or a god or . . . something. Hell, I don't know what to call it; I'm still on the fence about all this stuff.
Personally, I see an infinite universe as a possibility. But there seems to be, whether logically sound or not, a certain inclination, at least among some people, to believe it more likely that the universe had a 'source' rather than to believe that it simply always existed.