A bad alternator right out of the box? I experienced that once before on a boat engine. New alternator installed, never charged, survived for a little while on the batteries.

You mentioned you got it from Advance Auto (I shop there sometimes too). A couple years ago I bought a remanufactured rear window wiper motor from them for a Ford Escape. I was incredibly frustrated because the replacement didn't work which had me second guessing my diagnosis and wasting time. A day later I returned the motor to the store and they ordered me another, which worked! Moral of the story - never assume that a correct electrical part actually functions.