Have the Japanese invasion of Korea go much better for the Japanese. The Japanese up to that point did not have a very large Navy but could capture the Korean Navy. Once they own that wait for the Ming to start losing Mandate, have the Japanese take over China and claim mandate. From there they can restart the age old Chinese tradition of sending out tribute voyages. The best PoD would be for Admiral Yi to not become a Naval Commander. OTL Admiral Yi is the type of commander that if you read about him in an alternate history you would cry ASB.
From what I've read, the Japanese did have a large navy, just most of it was transports and their naval combat revolved around boarding while the Korean and Chinese fleets used much more long range artillery and they didn't have much knowledge of the currents around Korea, which is why the relatively small Joseon fleet was able to harry the much larger Japanese fleets with such effectiveness and the Japanese completely lost any semblance of naval superiority, despite numerical advantages. That's a naval tradition issue which could be altered with an earlier POD, of course, but that means capturing the Korean navy's not that viable a strategy without defecting naval officers. After all, the Joseon did have other notable leaders who could've performed similarly, it's just that Admiral Yi outshined all of them. The war was in two phases, anyways, and the Koreans lost most of their navy in the beginning of the second and still managed to win so it's not as simple as 'Japan has more ships.'
Other than that, the Japanese invasion's a bit overhyped. Sure, they managed to march from Busan to Pyongyang in a few months but it was against Seonjo's Korea, which had literally the bare minimum for any sort of southern defense possible, and they lost everything from Pyongyang to Hanseong in a few months due to poor logistics from advancing so quickly, rivalries between commanders (seeing as the clans had been fighting one another for a century, a bit hard to avoid between the best leaders) and civilian rebellions and militias. Even with more success in the war, the countryside will still need pacification, which is difficult with Korea's hilly, semi-mountainous and forested terrain in mind, and the Japanese themselves would inevitably get embroiled in a civil war the moment Toyotomi Hideyoshi (already old) dies as in OTL, making possible a reconquest of Korea by an exiled Joseon court.
It's worth noting that, even despite the Manchu's rather brutal treatment of their subjects, they were very generous to defectors and would marry off princesses to Han leaders. After all, they didn't have the manpower to take over China alone. The Japanese showed no inclination of that sort of behavior in their Korean campaigns (which is partly why the Koreans fought so hard once they reorganized and the countryside rose up in rebellion, mainly from the raping and pillaging) and Toyotomi Hideyoshi was a bit megalomaniacal, at least if he actually had ambitions on conquering all of China, the Philippines, India, etc.
Anyways, the Japanese would then have to fight the Manchu under Nurhaci in terrain they have very little experience in in order to march on Beijing, then assault the Shanhai Pass that the Manchu weren't able to crack without defection for any 'Shundynasty-open Shanhai' analog or fight the Ming navy on Chinese turf (same logistical, artillery, and terrain disadvantages as with Korea), all the while noting the everpresent disunity and hostility between the Japanese clans (OTL lasted 260 years after the Tokugawa's victory at Sekigahara). It'd be a massive expense of manpower and money and gives plenty of opportunities for the disloyal daimyos to rise up. Either way, they'd have to deal with peasant rebellions and militias and of course the Manchu. Even then, the logistics of managing all of China from Japan is just not quite feasible in the 17th century so yeah...not much of a way to even afford tribute missions, honestly, seeing as it'd take decades on decades to actually succeed in conquering all of China. The Manchu took decades and they were fantastically lucky.
As for the original prompt, like
@RousseauX said, Koxinga and the Three Feudatories had the best chance to crack Qing dominance and a more maritime-minded China. The Qing were not much interested in the navy so you need someone else.