The thing is that while Sengoku era Japan did have the capacity in terms of naval tech and institutions to do so, a mostly unknown continent populated by barbarians is going to way down on their list of priorities compared to Taiwan (which they actually planned to conquer), the Philippines (same, plus Spain was deemed a potential threat), and Southeast Asia in general (because of trade/anti-government ronin hanging out in local Nihonmachi merchant quarters there).
After that would come Manchuria and coastal Siberia, since that has similar resources to Hokkaido/Ezo and the Manchu were deemed a threat to Japan but also theoretically a good trade partner. Only THEN would they start poking around in the Aleutians and Alaska and eventually find the amount of ivory and jade in circulation among Native Americans there. And only after that would they reach areas suitable for large-scale cultivation, but maybe there wouldn't be too much time elapsed since they'd have access to European maps by then and would know they could sail south to reach Mexican ports and theoretically trade directly with Spain. My guess is if relations aren't terrible, then Spain would permit that and probably confine them to Acapulco.
But the Sengoku era Japanese weren't really about settler colonies, since they only did so in southern Ezo (which already had a history of Japanese settlement going back to the 12th century) and left the rest of the area with only temporary merchant quarters. Alaska is too distant for that, but you wouldn't see much more than Russian Alaska-style colonies, although maybe more numerous and larger because it's a good source of ivory and jade and the disease environment isn't as bad as Southeast Asia. So most "Japanese" would be allied Native American groups and a creole community.
I don't think with this model they'd get much further south than Cape Mendocino, and anything south of the Columbia River/Willamette Valley would be a string of coastal trading posts at the mouths of decent-sized rivers, and even these might just be places they visited every now and then to trade. That's why I think you need a radically different POD to get Japan interested in settlement colonies, and that just isn't going to happen come the Sengoku era. Granted, I think the number of Japanese citizens/mixed race people who identify with Japan might be substantial in this area given the experience of Quebec, potentially tens of thousands by 1800, plus with many Native American allies who might be a little better off TTL if they adapt agriculture come 1700 or so rather than the late 1700s. Pacific Northwest Indians learned farming and obtained crops from white traders, and although they never cleared forest or used fertiliser or let it interfere with burning oak prairies, they farmed potatoes and combined with muskets you had a similar situation to Musket Wars-era New Zealand).
Considering Sailors from China were the first native americans (and not Siberians) I think they could do it.
What makes you say China? Just because some Native Americans migrated not by Beringia but by hugging the coast doesn't mean they came from China.
I'm doubtful Japan had any capacity to build or maintain a strong enough navy to be able to reach the Americas, settle them and then defend those colonies against the much stronger European empires.
Not necessarily, given the only European advantage was naval technology and
maybe artillery. But so far from any major bases, the advantage is about even given the Japanese were efficient at producing muskets and were capable of innovating their naval designs as OTL history proves before sakoku was passed (and in the 19th century when faced with threats from Europe in the north).
The Spanish Empire's own record in the colonies shows they probably wouldn't have been able to seize a Japanese colony in California, let alone the Pacific Northwest, or even know it was there for potentially decades after it was founded (unless the Japanese decided to get in on the piracy game and attacked the Manila galleons as they passed Cape Mendocino). The currents and winds point the wrong direction from Mexico and they'd have to sail past the very dry Baja Peninsula across a rocky and fog-covered coast.
