It is rarely worth asking 'is it technically possible' with regards to programming tasks, as the answer is almost always yes (with some exceptions where there is a mathematical contradiction required to get to what you ask for). A better question would be 'do you have time to' or just going with a 'please'.

I would imagine that changing the 'start at level' trait to just provide a bunch of experience to the unit (based on the levelup costs), instead of changing it's starting level, would lead to a bunch of level-up choices when one finishes building the unit.