Financial Aid would very likely be enough for you attend USC, but you’d be throwing it to the mercy of the Financial AId office in lieu of a known quantity with the scholarship. I’m certain USC will make accommodations for you given your situation all the way up to simply wiring you your flight costs in advance, but you’d really have to communicate with them.
As a point of reference, if your parents make under 30-40k and don’t own a house, you’ll probably be paid down to 10k COA with grants, and the remainder can be covered with loans.