I would say that the best way for someone young to go into UPS w/out college education , is to do as Hoax mentioned: work P/T union until you are in place for a drivers position.
Go to school if you can, even if you are working FT hours.
Secure the drivers job down the road if/when it's available (make sure your driving record is clean) and try a leap into FT Supervisor role, where you can then maybe make your mark higher up.
The best way to advance at UPS to my knowledge, is to get experience, know your enemies and also follow the path of least resistance.