As I wrote, to leave the US you do not need a passport at all. There is no passport control departing the US.No. For leaving the US you need a US valid passport.
As a practical matter, of course, to fly from the US to any intl. destination you do need a passport, but that is because of the receiving country. The airline will want to see your passport before checking you in, but again that is on the basis of the destination country rules, not US ones.
Some airlines (probably some countries) are more careful about this than others. Before I was a permanent resident, I was stopped by the airline more than once.I have flown to Argentina dozens of times (always on one way tickets) and only once did an overly zealous agent ask to see my return ticket (this was at Madrid). I stepped on the side and put on hold a mock up award trip on the AA app. Showed the reservation (not ticketed) to the agent and that was it.
Sometimes a reservation works, sometimes they will insist on seeing a ticket.