Before the mini Ice Age in the 17th century, consequent famines, loss of the Mandate of Heaven by the Ming, and Manchu takeover, the Ming were well on their way to an all-gunpowder army.
So basically, WI the Ming get through the famine well, restoring credibility with the general population, and fight off the Manchu? How does Europe react to a Chinese army armed much the same way as they are?