Okay so I have pheels and theories about this girl.
I like to think that, the next day when Clint passed by her gas station and stopped in to see what was going on (See: Avengers Predude - Fury’s Big Week), he slipped this girl a SHIELD business card with a few contact details on it. She stashed it, forgot about it, and went on with her life.
After the New York attack, and the televised footage, she recognized Clint and remembered the information he had passed along. So she packed up, took her savings, and headed to New York intent on playing with the big boys. Being in the know, she had no trouble signing up for Junior Agent Training, and left the rest in her dust.
Phil and Clint both remembered her. They kept an eye out for her during training; they didn’t make it easier for her, hell no. If anything, they made sure she was pushed harder. Really saw what she was made of, and made sure the instructors saw it too. They keep an eye on her in the field, but won’t admit it to anyone.
Natasha doesn’t give a fuck, though. A junior agent is a junior agent, and they’re all bullet sponges as far as she’s concerned. No special treatment from Aunty Agent Romanoff.