There have been a few attempts to link East Asia and the Americas (after its initial colonization by Asians, of course) - fewer still have really gained much traction in academic circles.

The first one that comes to my mind is Betty Meggers' work in Ecuador, on some of the earliest ceramics found in the Americas. Working with the Valdivia ceramic styles in the 1970s, she argued there were strong likenesses in style and design to the contemporary Jomon people of Japan. However, it is much more commonly thought that ceramics in the New World were either developed directly in this area, or were an imported technology from the Amazon region (relatively accessible in this part of the Andes, as the mountains have wide, low passes that are easily traversed by Amazon and Andean people alike).

Another more controversial attempt came from Gavin Menzies' book 1421, in which he claimed Chinese explorers got to the northern American coast in, well, you guess what year :P However, Menzies is anathema to many academics, as he had very little hard evidence of this contact and ran with it anyway. He's been pretty thoroughly debunked on this subreddit already.

Finally, one intriguing, and much more reasonable, tale of contact between Asia and the Americas comes from a somewhat unexpected source: Polynesia. Chicken bones were found in a firepit on the Chilean coastline some years ago, dating back to before European contact (you'll have to forgive me, I don't have this source on hand at the moment). The chicken bones could only have come from Polynesian voyagers, who had ventured east, likely from Rapanui (Easter Island). It wasn't a permanent settlement, just a small camp before the voyagers returned (likely with an amazing tale of another continent out east), but would technically count as trans-continental contact.