If I wanted to obtain the Anti-Material Rifle, how would I go about getting the ball rolling?

Is that the Q-35 thingy? RepCon HQ for that.

You can also buy it from Gun-Runners off of Freeside. It's on random respawn, so you may have to visit the place from time to time to appear. Yet to see it drop from anything or find it anywhere else.

No sir, that's a plasma rifle...I want the Anti-Material Rifle, a sniper rifle.

Gun Runners outside of Freeside.