I have read about alternative starting methods from the era of the F-84/F-86. The jet blast of another, obviously running, fighter was directed up the intake of the aircraft to be started in order to spin its engine. A bit like a windmilling start inflight, although most likely involving rather big thermal stress to the recipient.
Someone who has been around at that time will surely be out in a second to correct me if needed.
In the situation the OP outlined, one might start small and move on then. Why not collect a heap of discharged car batteries. Insert one of them into a small car or truck (a follow-me, a baggage tug or similar should be available from Your description), push-start it, wait for its engine to recharge its battery. Wash, rinse and repeat until a sufficient number of batteries is charged. Then hook them up in series or parallel as required to achieve sufficient capacity and voltage and use this contraption to start a bigger engine. Firstly, a GPU to power up the aircrafts electric system and possibly as well the APU. Or if desired an air starter, depending on the aircraft to be used for the escape.
And from there, starting up an airliner should be trivial.