You can complete this challenge in the Mountain Base area of Tomb Raider. In this area you will come across a number of poster/banners hanging on the walls that you can burn by interacting with them with a lit torch in your hands.
Burn all five of the banners and you’ve completed the Non-Believer challenge. Here’s where to find the banners:
Banner #1: Coordinates – 712431, 3416298
Location. You’ll find this poster in the same room where you get ambushed by the Solarii (the room with the spotlights that blind you). Go into the smaller room directly across from where you enter to find the poster.
Banner #2: Coordinates – 712433, 3416288
Location. You’ll see this just as you enter the control room (right after the last Banner). Look on the wall to the right as you go in.
Banner #3: Coordinates – 712457, 3416298
Location. You’ll come across this banner when you come to the room with the glass wall where you throw a lantern into a gas-filled room to blow everything up.
Banner #4: Coordinates – 712443, 3416287
Location. When you first enter inside the base, at the first staircase you come to, there will be a door on the left side. There is a banner in here.
Banner #5: Coordinates – 712457, 3416287
Location. This banner is in the same room with the glass wall as #3.