Common themes shared by cultures that have never been proven to contact one another historically is, at least in theory, easily explained by neural evolution.
Interesting fact: in spite of having been split across vast expanses of different continents, mankind's brain patterns have evolved more or less exactly the same - different cultures with vastly different needs developed much the same technologies as they improved, with different techniques overall and different styles owing to their basic environments and how their cultures shaped up. They did, however, share several traces in common, whether in those technologies themselves or their cultural beliefs. That's why you have big firebirds both in ancient China and ancient Greece, even though neither civilization has, to our knowledge, ever contacted the other until relatively recently. Both also represent rebirth. That's also why Chinese and British dragon myths are different - both are big-ass lizards, possibly owing to the fact that lizards are reptiles and therefore often poisonous, though both also have different conotations, because of how each sees nature as a culture.
But in either case such similarities could be conceivably explained by identical evolutive paths insofar as our brains are concerned - much like babies have distinct steps in their growth patterns, like that age where they try to put everything in their mouths.