If the U.S. started the Great War Part III, it would probably be due to an invasion/takeover of a Russian-aligned country (e.g. Iran)

If Russia began the third big one, it would probably be due to either a) invasion of another European country (e.g. Finland, the Baltics) or b) some huge scandal that may or may not be truthful where American/European/NATO/whatever spies are found in Russian soil, prompting a justification to declare war.

If China were to start the war, it would almost certainly begin with either the hot topics of Taiwan or the South China Sea. I doubt the Chinese would risk a war for either though, and would only go in when the U.S. are distracted in some other war (e.g. if Trump goes in on Venezuela)