Are there any credible theories that the mythology of Atlantis stemmed from sightings of the Americas? If so, what is the full premise of the theory.
No, it's not, because Atlantis is a fictional place, known entirely from Plato's writings, and Europeans did not travel to the Americas until about the year 1000 or so. This answer as part of a larger AMA on pseudoarchaeology may be of some interest to you.
Edited to add this older thread as well.