Build a holy site, gain enough faith and great prophet points in the early going to earn a great prophet and form a religion as you normally would. From this point you can completely ignore religion for the most part. Let the other civilizations compete to convert your cities to their respective religions, since you need to have 0 cities following your own religion.
Many turns/eras later once you research the ability to buy a Rock Band unit, spend the faith that you've been slowly building through your holy site. The base cost is 500 faith. Each Rock Band will be immediately given a free promotion and 3 options to choose from. There is one specific promotion you're looking for that grants the band the ability to instantly convert the majority religion of any city to your founded religion. If you don't get this option you will need to try and earn additional promotions for the band, or buy more Rock Bands until you get one that has it.
There is a new future era civic called "Cultural Hegemony" which provides a wildcard civic that allows Rock Bands to choose from all possible promotions instead of just 3. So if you're having bad luck seeing the religious promotion, you can use this to guarantee it.