Growing up in the United States, we predominantly learn about our European roots. The Vikings sailed west to the Americas, as did Columbus, Vespucci, etc. What documentation is there of Asian countries sailing east to the Americas? Is that something they did before or after the east coast of the United States was settled by Europe? What conflicts, if any, did they have with Native Americans?
There is very little documentation of Asian countries sailing east to the Americas, because it's something that didn't happen. The famous Chinese "treasure fleets" of Zheng He seem to have explored immediate trade routes in the South China Sea, reaching maybe as far as the Malay Barrier, but they did not expand eastward and it's difficult to see how they would have.
If by "Asian countries" you're willing to stretch a point to include Polynesian cultures, there is some evidence that Polynesian explorers may have reached the west coast of South America, due to the presence of the sweet potato (an American crop) in the central Pacific, and what may or may not be a Polynesian chicken bone in South America, before European chickens were introduced. This is another thread about Polynesian-American contact.
Here's some more info from our FAQs about other theories of pre-Columbian contact: