Kristen,
Depends on the cadet program, do you have one in mind? ATP provides an entire list of cadet programs that are partnered with the airlines and flight school, you just have to check their requirements. Depending on the sought cadet program, you may start as soon as you get your Private Pilot Certificate or have to wait until you reach 500 hours total time; there may be restrictions like “you have to instructor for a partner flight school” etc.
Brady