Agree with Eastbay1K that online check-in (OLCI) is the way to go. Provided you check-in online and fly with hand luggage only, you wouldn't need to clear immigration since you are on international transit. After leaving the aircraft, walk through the long corridor until you see a sign for international connections. It's before the escalators going down to immigration. Follow the arrows and you'll be at a security checkpoint. Once you clear it, just walk to the main departures area. In my experience, with OLCI and hand luggage, airline staff will page you some minutes before boarding to check your travel documents.

If you can't manage to check-in online or you have luggage on the hold - run! 2.5 hours is quite tight for leaving the aircraft, clearing immigration and customs, walking to Terminal C (from where AM operates), departures passport control and boarding.