The BFG in Rage 2 is a weapon you can get for having the Digital Deluxe edition of the game. You do not start off with the BFG, but instead have to find it in the world. Check out this guide to find out where to find the BFG in Rage 2.
Where To Find The BFG In Rage 2
You cannot get the BFG until you beat the intro of the game. When the intro is done, you can explore the open world and find your BFG. Starting in Vineland, head north along the road until you get to this point.
Here a meteor will come crashing down just off the road. Get out of your vehicle and go check out the debris to find the BFG inside. You will only get three shots with it, so make them count. You cannot find more ammo for the BFG like other guns, but you can buy more ammo at Wellspring in The Torn Plains area on the map.
They are $1000 a pop so don’t expect to stock up on a ton during your playthrough. The BFG is best used when shooting next to multiple enemies and not directly at them. The blast will arc and kill almost everything it touches until it explodes at the end. Be sure to check back soon for more Rage 2 guides.
from GamersHeroes http://www.gamersheroes.com/game-guides/where-to-find-the-bfg-in-rage-2/