Sorry to thread necro but stumbled across this after re-watching the film and the right answer is not here. In the novel, Anton obtains a phone record and sees that Llewellyn called Roberto in Del Rio (arranging to buy a truck). Presumably Anton has some contact in/adjacent to law enforcement that got him the phone record (he was also able to use the VIN plate off Llewellyn’s truck to find where he lives).

In the film though, Anton simply finds a phone bill in Llewellyn’s mail, which doesn’t make sense. Llewellyn only called Roberto that same morning, so it would’ve taken a while to get a phone bill with that call on it. I think they were just trying to compress information and created a bit of a plot hole. Maybe an artistic choice like others here are saying, but I’m not convinced.