It's probably harder now than it's ever been, because Ming isn't total garbage like it was when it was tech 2 with inward perfection. Now it's tech 3 and its units aren't made of tissue paper, and you don't have the old looting upon which to fall back either. You can still win (I've done it with Mongolia, starting independent in a less-trashy religion should be easier), but it's going to be uphill for a bit. Still worth playing, but not a "first horde game" (IMO Oirat, Kazan, GH, Qara, and Crimea are easier first-time hordes. Timurids too if you force Tabarestan to release Persia to block the Persian revolt event).
Did you stay Buddist as Mongolia? I still haven't done the Great Khan achievement and felt like doing it as Tengri Mongolia. So far I couldn't succeed in doing the bankrupcy convert thing, since as Mongolia, every time I try it I get thrashed by either rebels or neighbours.