As we know it, the Europeans (the Spanish, British and French) were the first people of Eurasia to fully colonize North and South America, but what if another country had discovered it instead.
The Muromachi Period in Japan is still alive and on one of it's last legs, this is nearly a century before Columbus lands in the American continents and before the west had contact with Japan. In this alternate story, a Japanese explorer of noble blood, who sought permission of the Shogun to take a fleet consisting of foot soldiers and samurai to explore other Asian countries for close trade.
He set off landing in the tip of Russia, before going back to the Rising Sun Country with trade of tigers and gold. He then set off again twelve years later in 1402. This time however he brings more people, largely prisoners and curious peasants along with several samurai. The ship dubbed "Ryū-sen" sailed off beyond Russia and crashing on an unknown landmass, this landmass is what we call in our timeline, Alaska.
The royal explorer eventually come into contact with one the peoples of this land, the Afognak tribe on the island of Afognak. The Japanese first traded with these people, but eventually a large portion of the civilian and prison voyagers were abandoned to live with Afognak. These people traded cultural values and knowledge.
Eventually the Ryu-sen was repaired and managed to sail back to Japan, there it broke down completely and became virtually unusable. However, sparked by their discoveries, another group of explorers set sail with mentorship and directions of the previous explorers to find the Brown Lands as the Japanese referred to North America as.
Five ships set sail to Alaska, however they didn't all manage to succeed in their mission. Two ships landed in what would be known as California, while the other two landed in Alaska and traveled to the island of Afognak. The other ship landed in Canada, where they set up refuge. Most of the people from that point settled down on the lands.
Most of the Japanese explorers were male, so miscegenation was common between Japanese men and native American women. However, as the Japanese settled down, so did their rigid Feudal system. The samurai and nobles frequently conflicted with chieftains and warriors and villagers and peasants on both sides were sadly caught in the middle.
In California, the culture stayed more similar to original Japanese culture, due to the lower number of Native American tribes in California. Soon the Japanese became more familiar with wildlife. Two ships sent a total of fourteen black-tailed deer, fifteen elk, nine bison and three cougars back to Japan, where they became established species.
As miscegenation spread in the North, so did cultural change and became more complex. Much of the architecture was based of traditional Japanese culture, the same could be said about Etiquette. This so passed to the native Americans as they intermixed with the culture of Japan. However, most of the hunting traditions were adapted by native Americans. Fish like salmon and trout were a large part of some coastal village cuisine, while some slightly more mainland villages would hunt animals like deer and even bison.
In California, much of the population had scattered into small tribes and clans. Most of the Californians were nomadic due to the heat and lack of diversity in some areas.