The very earliest attempt to connect the Old and New Worlds via the lost continent of Atlantis occurred in 1552, when Spanish historian Francisco López de Gómara wrote in his Historia general de las Indias that America was Atlantis, and the proof could be found in the use of the syllable "atl" in both the works of Plato and ancient Mexico.
So far as I can tell, this ur-source for the Atlantis-in-America myth has never been translated. Here is the passage and a rough translation. My Spanish is not terribly great, so anyone who is fluent in sixteenth-century Spanish, please do let me know how better to translate this passage. [Update: Thanks to Felipe for correcting my translation! The corrected translation is below.]
“Pero no hay para qué disputar ni dudar de la isla Atlántide, pues el descubrimiento y conquistas de las Indias aclaran llanamente lo que Platón escribió de aquellas tierras, y en Méjico llaman a la agua atl, vocablo que parece, ya que no sea, al de la isla.”
But there is no dispute or doubt what was the island of Atlantis, for the discovery and conquest of the Indies simply clarify what Plato wrote of those lands, and in Mexico they call water atl, a word that seems like, if it is not already, from the island.
Source: Francisco López de Gómara, Historia general de las indias, vol. II (Calpe: Madrid, 1922), 249.