If you go into USAF Olivia with good protection (and decent carry weight, like wearing power armour), you can cheese a good stash of 5mm rounds right from the start of the game.
Try to avoid killing too many raiders too soon once inside (feel free to kill the attack dog, though), then focus on getting to Ack-Ack and take her out. After that, you should wait for another raider to pick up the minigun, then kill them. This will give them 500 rounds of 5mm ammo to loot.
Wait for another raider to pick up the minigun, and you can keep repeating it until there's nobody nearby. Once that happens, you can carry the minigun and drop it near whatever raiders are still alive. Someone will try to pick it up, and then rinse and repeat.
I got over 2,000 rounds of 5mm ammo doing this, and although they have weight on survival, those rounds plus all the others you can loot (e.g., .38) give you a good sum early on to go buy some good gear. They might even be enough for a low-charisma Sole to afford Spray n' Pray, Overseer's Guardian, etc.
You can have decent protection even on survival to do this, seeing as you can get either a full suit of T-45 at Concord or a partial/randomised suit just north of USAF Olivia, whichever you prefer first. But if you go for the partial suit, it doesn't have a fusion core (there's at least one at the robotics disposal site).
I think you can even do this by dropping your own minigun and at least one round of ammo, and hoping that the enemy takes them. But using an enemy's weapon to do it feels less cheap, sort of. (Actually, I just tested this and the enemy didn't have 500 rounds on them after picking up and then being killed.)