How do I get Rookies late in the game?
You can recruit rookies from inside the Avenger. Click on "Armory", then on "Recruit" and you get a list of wannabe alien killers willing to join your cause for 25§ each.
Another small possibility:
Occasionally small scanning areas will pop up, similar to the ones you can scan for Supply Drops and other resources that will offer recruits. This can occur very rarely in late-game but it is a possibility that can also save you some supplies.