In a sense, that is sort of what Columbus was trying to do.

He expected to land somewhere near "Cipango" (Japan) or "Cathay" (China), claim any land discovered for the Spanish crown, and spread the Christian faith to the local people and their leaders. He was under the impression that the Greater Antilles were either Japan, or at least somewhere near to it.

There wasn't a clear "colonization" plan at that point like we might see with later colonial charters and corporations, but Columbus was granted viceregal authority over any new lands claimed for Spain. There was a colony set up on his first voyage, but only because the Santa Maria was wrecked due to someone allowing a cabin boy to take control of the ship Christmas night. So several of the crew members got to say behind and build Spain's first colony in the New World at "La Navidad" while Columbus returned to Spain with the two remaining ships.

So "colonizing Japan" wasn't really a specific goal at this time by Spain, since it was questionable as to whether Columbus could actually reach Asia, let alone set up Spanish colonies. But he was given authority to claim land for Spain and to govern any of those lands, so establishing something akin to a colony was certainly not out of the question.

The Spanish tried invading the Moro Sultanates for three centuries but failed. Spanish tried invading Cambodia in 1597. They were defeated. The Portuguese were defeated at Xicaowan by China in 1522. The Dutch tried invading Cambodia and attacked the Nguyen Lords in 1643. They were defeated. The Dutch tried attacking China but were defeated in 1624 at the Pescadores, in 1633 at Liaoluo bay and in 1662 at Fort Zeelandia.

That should tell you why none of them tried to invade countries further than that. They couldn't.

Oh boy, I would love to read about a European direct attempt to colonize Japan during the Sengoku and early Edo eras. I wonder how "well" that would have turned out for the colonizers.

Follow-up question, are there any writings by Europeans on their impressions of Japan's military prowess during the Sengoku era? Did any European power even consider taking over Japan?

I'm on mobile, so apologies for brief. Essentially, no. The reason is because the first Europeans to come to Japan, the Jesuits, were very impressed by Japan. There was the recognition that they were a civilized people, not like backwards natives of other places that needed colonization. Also, the people that initially went to Japan were mostly Portuguese, they probably did not have the manpower to do so either. Asia was basically the first region they got to where they couldn't just take over.

However with European colonization of other nearby countries there was very much the fear of European colonization, a large reason behind the 26 Martyrs under Hideyoshi. Worth noting that at one point the Jesuit leader did seem to consider a coup vs. Hideyoshi by allying the Christian lords, but iirc he realized this was stupid pretty quickly (or perhaps his superior Valignano did, can't remember without sources).

By Tokugawa it was probably realized as a very unlikely thing to achieve and to my knowledge neither Dutch nor English seriously entertained the idea.