Regarding the same or similar 'cosmology' cropping up in different cultures, people travelling from one country/area to another is not something that only started with Thomas Cook's Travel Agency. People have been toing and froing since time immemorial, and carrying ideas and beliefs with them. Some of these ideas and beliefs caught on, some didn't.
I completely agree that there are well-documented migrations of creation traditions, such as from India to China, Japan and Korea in the early centuries A.D.. There are also many well-documented similarities of traditions from cultures who are considered to be too far-distant from one another to have reasonably allowed that. Again, it is not so much the cosmological themes or forms that present a problem, but more often the complex symbolism that consistently attaches to those theme or forms that point to a common source. During the 19th century, many attempts were made to trace a credible migration route from one culture to the others around the world, but all ended up meeting with intractable contradictions.
Then there's Sherlock Holmes who said so aptly, 'What one man can invent, another can discover.
The same problem presents itself with theories of parallel development. For example, any culture whose primary building material is stone will likely think to
stack stones up to create pyramids. But there is nothing in that impulse that would lead them to conceive of the pyramid as a woman lying on her back (with the pyramid playing the role of an expanded womb), or to associate the four faces of the pyramid with star groups used to regulate the agricultural cycle. To my way of thinking, the symbolism implies a shared cosmological system.
Point is, a common source in the form of ETs or a Lost Continent is not required.
However, when disparate cultures with matching cosmological systems each overtly credit a non-human source, my view is that it's fair to take those statements seriously. For me, it rises to the level of corroborated testimony.
We need to give peoples of the dim and distant past a lot more credit than we do today; they were just as intelligent and resourceful as us. It is an insult to our remote ancestors to believe that they needed help from technologically-advanced Aliens to achieve the things they did.
Again, its the cultures themselves who consistently tell us they had help, not us imposing the idea on them.