Declare a no-CB war on one of the two neighbours on the earliest date, May 1st.
Win a war.
The Three Mountains
Europa Universalis V
People in Paradox have the sense of humor. Once an incredibly difficult achievement in EU IV, is actually very easy in this iteration of the game.
Pick one of the three nations on the island and conquer the remaining two. It's that easy.
I did it as Chuzan, as they had the biggest population.
Achievements
Defeat their small army, occupy the province, sue for peace. Now you control two locations.
Wait a bit for integration of the the new province, somewhat increase control maybe, recover levies. Can be done along with creating a spy network and actually making a casus belli (Destroy Enemy) to use it this time.
Conquer a location.
The strategy for the second war is the same: declare, win one battle, occupy, peace out. Then open the government panel and form Ryukyu. Done.
Form Ryūkyū.