The private, large universities have some funding, but they tend to be need-aware, which means your ability to pay will be considered for admission.
My sister attend USC on a full ride more than 20 years ago, but she wasn’t an international student. Things and costs have changed. My son was admitted, with exceptional stats, but all they “could” guarantee him, as a NM winner, was ½ tuition. With remaining tuition and housing, we would still have to pay $40k+ per year. That’s what they “could” do.
It sounds like you need a full ride, so there are very few universities that have that kind of funding. There are only 5 schools and they also happen to be the toughest and most competitive, with very few seats.
Chances, as an international student, who needs full financial aid, are extremely small.