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Some dragons cannot possibly exist (e.g., a giant, flying, firebreathing, reptile that is non-magical cannot exist because giant flying creatures contradict the laws of physics on Earth). Some dragons do not seem to exist (e.g., magical dragons do not seem to exist because magic does not seem to exist, although, if magic does exist, we'd need to know more about it before we could say that magical dragons could or could not exist). Some dragons do exist (e.g., the komodo dragon exists as a living species, and the Chinese dragon exists as a cultural theme).
If you want to find out if something exists, you're gonna need to be more specific. Not being specific is why someone will say that something is unprovable (e.g., God is unprovable more often than not because it is so vague and few people bother to say whether or not God is in the system of the Universe, and when they say he is outside that system, we cannot disprove him because we do not have a definition of supposed the external system)—define the thing and, IF we have a suitably detailed definition of the system that it supposedly resides in, we can figure out if it even could exist. If it could exist, then you just need to narrow down the possibilities of where in the system it would reside, and then you can go have a look and you'll either find that it does currently exist or does not currently exist.