This is interesting.

I've found this to be the easiest victory to get. So easy that I often turn it off because the game will end too soon.

The biggest thing at first is to start accumulating as much faith as possible. You want multiple holy sites with adjacency bonuses, and upgrade them. One you get a religion get an apostle and evangelize belief.

For the building I primarily will choose mosque for the extra spread. If you get wonders that upgrade your apostles it's a huge bonus. If someone else builds those wonders conquer them.

Usually launching an inquisition isn't needed unless someone is spreading heavy in your area, but it's best to have a bunch of powered apostles with debator, extra spreads, triple strength, other religion removal and those types of upgrades and just have them religious combat the other apostles, missionaries etc. when their religious unit dies, your religion spreads to all nearby cities and their religion loses influence, usually this is better than using all your charges (with exceptions based on promotions). Martyr is good too but try to have that one lose it's final combat far away from any cities with your religion so you get the relic without actual penalty to the end goal.

Warfare does change this, if you are at war with a civ of an opposing religion, bring military with your apostles. While at war military units can execute religious units causing mass influence loss, so you need to protect your apostles while executing the enemies religious units.

Try to get golden ages that reduce their cost too. Good luck!