Just curious, have you thought of using your GI Bill to pursue your college education while perhaps working at UPS as a pkg handler, thereby securing health benefits and furthering your education which could present you with more opportunities for employment. I thank you for your service and now would like to see you take advantage of one of the benefits to which you are entitled.
Now, to answer your question, if you are intent upon working at UPS and would like to someday become a driver, the best way is to start on the inside and work your way up, knowing that this takes time, the amount of time depending upon where you are located. I was hired off the street and became full time after just 11 months in 1989 but that is typically not the case today--it is more like 5-6 years in my center, more in some, less in others. Also, our contract has a ratio of inside to outside hires that are promoted to full-time--I believe that the new contract has set the ratio at 6 insiders to every 1 outsider to be promoted to full time (BC regulars please correct me if I am wrong) so you can see where starting on the inside is to your benefit. Your Army training will both come in very handy and greatly frustrate you if you do come to work at UPS.