usualguy:
yes I know I am from the old school where you start as a FI, get your hours then move to the airlines.Many of my friends are in the same boat.
I am from what you call the old school also.
Flight instruction, bush, charter, multi, turboprop, small jet, then B737NG.
That's why I say you are missing a few step. I wouldn't aim directly at the A320 in your situation. Next step would be bush flying on single or twin piston, then turboprop, an so on....