Apparently over 200 Japanese people were confirmed to have crashed/landed in Western North America from the 16th-19th century due to how strong the currents are, and there's genetic evidence of some Japanese migration and/or presence in Western NA. Might that be a good way to achieve something like this?
Very difficult. I used to like this PoD, but it relies on the sailors surviving along with the cargo being useful. By this I mean agricultural goods (buckwheat, millet is good for most of the West Coast including much of Alaska, rice is good up to southern BC assuming it's a hardy breed used in Tohoku) or maybe the wheel. Then you need the Japanese sailors (who will almost certainly be enslaved upon arrival) convince their masters of the use of these goods AND be able to show them how to use it AND reproduce it. Agriculture produces extra food, which in those societies would be tended by their slave wife (assuming they can get one). Maybe the exotic new plants (assuming the first harvest yields well) convinces the noblemen/chiefs to plant more, with the sailor's advice in mind, which later convinces experimentation on plants already utilized (wapato and camas being the big ones). The wheel encourages more weaving and helps the economy which leads to animal domestication.
This also takes a PoD on the Japanese side, one where they take Hokkaido early (as in Heian period or so early). But that's not particularly early since we have only a millennia at most until Europeans show up. Not much time for the development needed to make a truly profitable trade (since why go to the PNW when there's still easier sources of fur, tin, etc.). And as you can see by how convoluted that whole scenario is, it's highly improbable. Elements of it are still useful, but Japanese castaways aren't going to kickstart a civilization. A far more likely PoD is said civilization kickstarting itself.
Or maybe go earlier and ditch the Japanese entirely and have more sailing in Jomon/Yayoi period Japan which results in more contacts with the people north of them in the Kurils and Kamchatka who in turn are also sailing more so they're in contact with the Aleuts who are (or will later) be in contact with the Tlingit and Haida. This exchange would bring a lot of technology into the PNW (and beyond) and crops used by the Jomon and Ainu with it. Best time would be the Roman/Medieval Warm Periods since agriculture is possible further north.
That could be fixed by having some of the land be a bit higher than in OTL. Or as I said before have one of the asia nations found the new world and set up something. I have no idea when that could be maybe in the middle ages. The east is as it was in OTL but the west is far more advanced technologically. So I could easyly see the US not be as big in this timeline. That is if the US would even exist in a world that has the North American continent as technologically-advanced as it would likely be.
Land bridge is overrated, since it wasn't the Bering Strait but naval technology that inhibited contact and trade. Not that they didn't do a great job with what they had (Aleuts, Inuit, and many PNW groups were expert seafarers, that's how they crossed over to the Americas to begin with), but it's hard to bring your herd of reindeer across in a kayak. And since the locals don't want you there, why bother going for the risk? Otherwise it's likely the Chukchi or some other Siberian group would've displaced group after group in the Subarctic.
As noted, there isn't much reason for Asian nations to find the New World, and if they do, not much reason to settle it. The Basques, Bretons, etc. didn't care to settle Newfoundland after all, and the Aleutians aren't very inviting as anything but a temporary fishing camp. Plus they're all barbarians anyway, so why bother with distant barbarians?
But even if there was, say, Japanese or Chinese colonialism there in the 1200s, the locals will give them one hell of a fight (since technology on the Asian side isn't as good as the 16th-19th century Euroamericans), but they could be swamped by sheer numbers (Japan and China were often times "full" before the inevitable plagues, famine, and war broke out). Not much tech will spread, even if it's likely that Amerindians will get a better deal than OTL.
That's why you need better civilizations on the other side, to convince the Asians to want to go so far in the first place.
