When i started my plan was to go with Japan, unify the country, invade the mainland, colonize the Americas, and bump the Meiji Revolution up a couple hundred years.
It seems that when the game first came out that would have been an entirely reasonable thing to try. However from what i've been able to piece together almost every patch to the game has had some component to nerf that possibility.
Apparently in the original version Westernization was something that was relatively easy to do and gave you huge benefits. From what i understand based on old forum posts when you Westernized you not only got to switch to the Western military units but you also got a huge tech bonus. It sounds like maybe you were put in whatever equivalent part of the Western tech tree you were on your own tech tree. Which meant that people would start as the Native Americans and max out their own rather sparse tech tree, then Westernize and suddenly be as powerful as the Europeans.
So the developers decided to make Westernization a lot harder and make the benefits a lot weaker. It definitely seems like they went overboard with the nerfs in both areas, and combined they make Westernization both very difficult and not all that beneficial.
First they made the requirements for starting the Westernization process more strict. Having a European set up a trading post next door is no longer good enough, you have to have a core province next to a core province with the Western tech.
Then instead of adjusting where you ended up on the Western tech tree after Westernizing they decided to make it impossible to Westernize unless you were "far enough" behind the Western nation(s) you were bordering. And "far enough" in this case is rather extreme. Almost a dozen levels for Chinese tech nations.
And then they made the process of going through Westernization harder. Before you already had to deal with a decade or more (possibly _much_ more) of increased adviser costs and increased revolt chances. But on top of that they added random events that could set the process back if you don't take some other big penalty instead, and worst of all put a penalty on the rate of conversion based on the income of your nation. The more income you have the slower the process goes.
So once you've done all this, you get, well, not as much. You no longer get to replace your old units with Western ones. On top of that (and i have no idea if this is a change or not) you apparently lose all your old buildings and have to rebuild them as Westernized equivalents. Which really seems like the worst of both worlds. But hey, your tech costs are now 60% cheaper! (Or rather no longer a 60% penalty, at least in the case of Asian techs.)
So if you want to Westernize now you need to _not_ advance much first, and you don't really want to build up your infrastructure because A: high income will make the Westernization process slower and B: you'll just lose it all anyways. And if possible you want to stay relatively small.
So at the point i discovered this i decided to stop my mainland expansion, save up my Monarch point instead of advancing my tech, and try to rush across the Pacific and meet up with the Europeans in the Americas so i could get the process over and done with as quickly as possible.
So how does one go about colonizing as the Japanese, or any of the other powers that weren't big colonial powers in actual history and thus have not been given pre-set advantages by the developers?
One of the first tricks was to sign Fleet Base agreements with people to extend your colonization range, and in particular signing them with the Native American nations. Okay, i admit that is a little cheesy, and i can kind of understand why they decided to nix that possibility in one of the early patches.
I had two options i could follow, north-east up to Kamchatka, over to Alaska and down the coast, or south-east to Micronesia, Wake Island, Hawaii, and then Mexico.
I decided to go north-east because that seemed closer and easier. It wasn't until i finished colonizing Kamchatka that i discovered the distances up there are all kinds of messed up. It kind of looks like they assigned colonization distances based on the map projection rather than the actual distance, and even in that case it seems a little extreme. They did group all the Aleutian islands together, so perhaps the distance is based on the center of the province rather than the closest island, which seems a little unfair.
I did stumble across a trick you can do at that point. You may not be able to colonize the Aleutians, but you can drop a small army with a Conquistador off there and have them explore down the coast. So i did that and eventually encountered the Shoshone tribe. Since i'd maxed out the Exploration Idea i was able to declare war on them automatically and did so. It didn't take long to conquer all three of their provinces. Then i (luckily) saved the game before deciding what to do. At first it seemed like it would be easier to just claim their territory for myself, so i tried that out. And then i discovered that you can't core your provinces unless they're in your "core range", which i presume is either the same as or very similar to your colonization range.
However i did find suggestions on the forums that you could vassalize the Natives and then annex them later and get the territories as auto-cored, so i went with that option.
However since it would take ten years for that to be viable i kept exploring. And since i didn't have a lot better to do i decided to start down the southern colonization path and started colonizing Guam, with the goal of eventually getting an ocean route to Mexico and maybe grabbing Australia.
I moved south until i found the Aztecs blocking off Mexico, then over to the east coast. And then suddenly a Castile colony popped up next door to the Aztec empire!
So i declared on the Aztecs. I had to compete with the Maya who were invading them at the same time, but i ended up vassalizing them. I was a little concerned because they had 6 or 7 provinces, and from what i've read if you ever control 5 or more provinces in the same "colonial region" they turn into a "colonial nation", and i'm not sure if that would count for the purpose of bordering for Westernization. However i figured i'd give it a go.
So fast forward a little over 10 years until the "mandatory annexation waiting period" was over and i'd gotten relations recovered enough for it to be feasible. ...at which point i discover that you can't annex someone who's outside your colonization range either!!!
So at this point i've got a couple choices. Keep pressing on, trying to colonize across the south pacific until the Aztek are in colonization range, then hope that when they turn into a colonial nation it will still count as "bordering". (And if not, then i cry.)
Or i could reset back to the point where i decided i was going to save for Westernization and start spending those point on tech instead, making a bigger push on the colonization path. The flaw with that plan is that the main rate limiting factor there is the speed of colonization itself. Unless i can push colonization range up high enough to get to Alaska there's not many shortcuts i can take.
Or i could reset back to the point where i started the colonization process and go all in on the southern route. Or alternately, i could instead try crossing across India and the Mid-East, by some combination of colonization and vassalage, and into Africa. Where i would either meet up with some European colonies or could swing up towards Europe itself. However although that might by technically simpler than going across the Pacific it seems like a lot more work.