Can I go to Airborne School after basic and AIT without an Airborne contract?

Hell yeah, you can. When the Ranger recruiters come to your AIT just volunteer. If none are scheduled talk to your platoon sergeant in AIT to get an Airborne physical and a school slot.

When I got to AIT at Ft. Gordon (Sig Corps) the first day of in processing the ranger liaison pulled the few of us with Opt 4 or Opt 40 contracts plus everyone remotely interested to the side and put us in a horseshoe and chatted with us. Basically when you get there you talk to the liaison, get your physical and med pros taken care of and tell your platoon sergeant as early as possible. They will set you up to get a spot in airborne in stead of pushing for your orders to your first duty station. Its damn near guaranteed to get it as long as you dont become a sloppy soldier during the long ait wait.

Typically in 68w AIT you will be offered RIP opportunity somewhere past NREMT exams. You have to be doing really well for cadres or drill instructors both physical fitness and exams to be accepted