From a big picture strategic level - any aircraft, very quickly; 756, quickly; 777/787 not long but not quick

From a tactical, new hire perspecitve - there's a lot of luck involved. They haven't run a big bid in several months and I suspect there's a lot of pent up demand to shuffle bases. That will take a few months to be satisfied when big bids resume. Time your class date right and you might get to dulles before you finish IOE. But get it "wrong" and it might drag for some months.

If you live in DC area, they have nearly hourly service from DCA to EWR that's rarely full because it's a slot-squatting operation.