Christianity spread first in Europe, and in general, by offering the toiling classes something to look forward to besides suffering. For a bit charlemagne tried to spread it at the tip of a sword but that was more the exception then the rule.

It spread through the America’s partly through violent colonization but also for the above reasons and the natives desire to assimilate into the new ruling class.

It spread and continues to spread through sub saharan Africa mostly due to heavy evangelical prosthelyzation from the west. By the time of African colonization the Europeans were directing there violence towards securing resources, not securing converts, even though that was the excuse they often gave.

Christianity may not be true but it is an attractive world view. Yes you may suffer the cruelty of others on earth but that is temporary, at the end of it all you will spend eternity in paradise and your torturers will be sent to hell. There’s a reason Marx called it the opiates of the masses, and the promises of opium don’t need to be true to sell.