It's not quite clear just where this happened, however. The map we keep seeing at the beginning of the show is of South America, and Mayans didn't extend quite that far south, as far as we know. But that sort of blurring of history and geography is ok in a narrative like this.
And, indeed, the story takes another nice jump away from the mystical into the plausible, much more satisfying as far as I am concerned. The high priestess knows Da Vinci's name and face. And she can speak his language. How can this be? The answer is that Da Vinci's mother sailed across the Atlantic and educated the priestess. Nice touch.
In real history, there likely were numerous voyages across the Atlantic prior to Columbus. Certainly the Vikings did it - their presence in North America around 1000 AD has been confirmed by carbon dating of artifacts. (I'm hoping Vikings on the History Channel someday get around to this.) And the Phoenicians had the sailing know-how to get across the Atlantic, too. So it would not be shocking to learn that a few ships from Italy made the voyage before Columbus, and one included Da Vinci's mother.
Another nice touch was including Amerigo Vespucci on the Da Vinci ship. In reality, he arrived in the New World just a few years after Columbus, had something to do with a Medici, and as we know had the whole New World named after him - the Americas.
Da Vinci's Demons continues to shape up as good alternate or secret history.
See also Da Vinci's Demon's 2.1: Science Fiction v Fantasy ... Da Vinci's Demons 2.2: Renaissance Radio ... Da Vinci's Demons 2.3: Submarine ... Da Vinci's Demon's 2.4: Copernican Revelation
an ancient voyage to the New World in The Plot to Save Socrates