I wanted to jump in here and comment on this interesting topic. I've studied the subject of pre-Columbian American exploration, Atlantis, and most types of pseudoscience for most of adult life.
Two things, first somewhat unrelated to the topic at hand:
1) For some truly mind blowing stories relating to pre-Columbian exploration of the New World try searching Google with any combinatinon of the following: Knights Templar, Money Pit, Oak Island, St. Clair/Sinclair. It harkens to themes and ideas presented in the Da Vinci Code and countless Masonic/Grail legends done over the last 150 years. (I happen to live within sight of George Washington's Masonic Temple in NoVa
) (is this common knowledge? If it is sorry.....)
2) I don't think it was mentioned earlier, but Admiral Zheng He's voyages and those ostensibly funded by Zhu Di (as in official state sponsored explorations only here) have been well documented from my study of the subject. I cannot speak to privately funded ventures of unknown 'adventurers' (of which there were a great deal during that period of imperial history), but the official state voyages of the Admiral and those associated with China's brief stint as a maritime empire dealt with Polynesia, Africa (they got far there), and Arabia.
I have read articles that indicate the possibility of a Chinese landing in California and Baja based on something like left-behind shipping pots or something of the nature (its been awhile since I researched this). But IMO the Zheng He/Zhu Di/official state sponsor link is not credible. I unfortunately can't point to many sources for these comments (yet), but I researched this and other subjects like the Vikings in the New World, Atlantis, and others for a good chunk of my college career. Vikings, British Islanders (Sinclairs and maybe Irish monks) reaching America ..... credible. Servants of Egyptian pharoahs and Zheng He not as much.
Respectfully,
C.I.D.
Edit: Forgot to mention, I actually studied the Zheng He era while I lived and studied in Beijing a few years back. I heard some cool stuff about his travels, but America wasn't one of them. ....... I switched majors a lot in college