Well, I'm pretty sure Toyotomi Hideyoshi invaded Korea because he saw it as the stepping stone to China. From there, he apparently wanted to conquer the world. If there's a man who is going to conquer China pre-1900, it would probably be him.
The idea could possibly be that Toyotomi decides to build up his navy and then invade Korea. It could be combined with a lazier Ming Wanli. For the last two decades of his reign, he refused to meet with ministers completely. In this world, he might refuse to participate in affairs of government from the start. After Toyotomi conquers Korea, he would predictably move on to China, which might not resist effectively given the corruption in government.
Still China is huge, and even when the Emperors are terrible, their ministers can still be effective. Toyotomi would probably get bogged down eventually, and probably die before he can see to the project's completion, at which point Japan goes back to civil war.
Dorgon did NOT get bogged down. Nor did the Manchu fall to civil war after Dorgon was disgraced. Nor were the Southern Ming officials any good.
The OTL Toyotomi campaign was 1592...1598. 6 years.
On 18th May 1644, the Qing were firmly outside Great Wall of Shanhaiguan Pass, Beijing was held by Chinese Shun Dynasty and Wu Sangui was loyal to Ming Dynasty.
By 5th of June, 1544, Beijing was in Qing hands.
In 1645, the Qing wiped out both Shun Dynasty and Southern Ming - Nanjing regime seems to have collapsed in less than a month after Qing attacked in earnest. In October 1646, Fuzhou was captured while within January 1647, Qing conquered both Southern Ming holdouts in Guangzhou and Daxi dynasty of Sichuan.
In short, by May 1647, no one resisted Qing in China save Southern Ming Yongli emperor chased into mountains of Southwestern China, and Koxinga who was chased into offshore isles and could not hold mainland major cities.
Note that the Qing peace was based on the submission of 3 Feudatories. Wu Sangui did rebel in 1673, but the Qing managed to pacify the Feudatories by 1681 or so, and Taiwan by 1683. And hold China for 200+ years.
Qing had conquered basically whole China in under 3 years, without any major defeats or serious and sustained resistance.
Qing approached overland from Northeast with cavalry forces. So had the Wuhu in 316, so had the Jurchen in 1127, so had the Mongols in 1211.
Southern Jin and later Southern Dynasties held out against the barbarians for nearly 3 centuries. Southern Song stopped the Jurchen for over a century, and Mongols for over 40 years. Southern Ming, as noted, collapsed in a matter of months, maybe less.
Japanese did have horses, as did Chinese, but they did not have mass Manchu and Mongol cavalry as Qing did. On the other hand, Japan had a navy from the start. Which parts of China would Japan held first, where would they chase holdouts and how would they deal with them?
How could you butterfly a successful Japanese conquest and long term holding of whole China?
1) Get Ming to collapse earlier - so that Toyotomi Hideyoshi meets a weaker adversary, like Qing did in OTL 1644
2) Get Japan to try later, on a more opportune time - or try again. Somehow persuade Tokugawa Shogunate to invade China - or get another regime in Japan, like Toyotomi restored after 1614, or Shosetsu after 1651, which makes changes in foreign policy.
Which of these are probable?