As you know it, the Chinese Ming Dynasty was fighting for survival against fiscal turmoil and peasant rebellions in the late 16th century until their fall.
The Chaos and Civil Wars in China practically invites a slew of neighboring conquerors coming to prey upon the fallen nation, but the Tibetans stood out. Under the 4th and then the 5th Dalai Lama, they end up conquering China using a combination of military might and Buddhist propaganda, that the 5th Dalai Lama finally end up taking his seat in the Forbidden City as the first Arhat-Emperor (Luohan-Huangdi), and from the point on, China is under the rule of Tibetan Buddhist Theocracy.
Sure, unlike what is basically every other dynasty of China, it was believed that the Arhat-Emperor, that is also Dalai Lama, reincarnations of Avalokitesvara Bodhisattva, that will reincarnate after death and this the line is believed to be an unbroken series of reincarnations.
Now, there are indeed other competitors in this regard, there are some Mongol Warlords, some Manchu Warlords, Japan enroachments is within memory, and even the short-lived Shu dynasty... And considering the age, maybe Europeans want some say in this matter too...
What if the prize of Mandate of Heaven was not attained by Dalai Lama but by another, more secular pretender?