A while back, I read a book called 1421: The Year The Chinese Discovered America. It has since been renamed as the scholarship has expanded and shown evidence of Chinese fleets from 1421-1423 discovering not only the Americas but also Africa, Antarctica, penetrating into the Arctic regions, exploring into the Mediterranean Sea and the north shores of Europe, and Australia.
There is evidence of "white" people in the Americas before Europeans were -- most notably encounters with settlements of "fair-skinned" peoples by European explorers penetrating as far inland as Colorado and Wisconsin. Compared to the Native Americans that would have been encountered by the European explorers, the descendents of Chinese colonists would have appeared "fair-skinned," and other physical differences between Europeans, Native Americans, and these people may have been mitigated through a few generations of intermarriage or the Europeans may simply have never met Chinese people before and did not know what to compare them to. Then, there are many similar elements of worship between Native American worship and theology to Buddhism and many similar trappings between Buddhist and Aztec priests, a sudden improvement in pottery techniques of Mesoamericans in the fifteenth century, and legends of the foretold return of the white-skinned explorers to the lands controlled by the Aztecs, which caused Aztec to initially fail to defend themselves from the Spanish conquistadores. There are artifacts like lacquer bowls and the sudden appearance of chickens as a food source about two generations before the documented dates of European arrival. None of this definitively proves that the Chinese sent explorers to the New World (and indeed all over the world) before the Europeans did, but it does raise the possibility as a plausible theory that neatly explains some otherwise very uncomfortably odd facts.
The link above points to a news article that I found through FARK this morning, showing a Chinese map from 1763 that purports to be a copy of another map from 1418 -- three years before the author of The Year The Chinese Discovered The World claims he can prove that the Chinese sailed to America. It kind of makes sense that the Chinese admirals would have sent out reconnaissance ships before investing such huge resources in the "Treasure Fleets," which were, up until the nineteenth century and the advent of steel and steam power, the largest ships ever built. The ships were intended to foster trade with foreign peoples and start colonies of Chinese in new lands; but before sending colonists and merchants to other places, it would have made sense to have found out if there were people there with goods worth trading for, and lands worth colonizing, in the first place. If the map is truthful in claiming to have been originally drawn in 1418, then that would have been the result of these voyages of reconnaissance. A reconnaissance trip would have been considerably less expensive and risky than sending the treasure ships out into uncharted waters.
The book is well worth the read and while it may not meet every test for absolute scientific or scholastic rigor, it is not harebrained, either. The book candidly deals with the failures of the Chinese navigators as well as their remarkable achievements, and the reasons why the Chinese economic and political system failed to sustain the trading and colonization efforts, and why the Chinese did not preserve this knowledge to provide future generations with better documentation of what happened. Some of the "evidence" cited is questionable -- for instance, the author's theory that the Bimini Road was a Chinese drydock -- but along the way it throws out some very interesting documented evidence for consideration, it is an intriguing and plausible idea.