I just finished playing a game as Manchu, and found that Ming seemed unduly reluctant to attack me until I got pretty big. (I was allied with Japan for much of the time, which helped quite a bit.) I made a point of doing nothing to provoke them because, as you note, they're vastly more powerful than Manchu.
I did do a lot of colonizing and, to be honest, it was just about the only good news I had for much of the period. (Expanding into Ming wasn't an option, Ming was guaranteeing Korea, so expanding there was not an option, and those ghastly Oirat provinces are so poor they will pull down your already unimpressive Manchu average province value, and clobber your research.) Many of those territories north of Manchu have valuable resources -- I got two gold and two fur out of my first six colonies. Once you have colonists, there are also some missions that give you immediate cores, which is cool. They ended up increasing my research speed, although the cost was a big drain on my census tax receipts.