Big 4 firms do not value what school you went to, but rather your performance in school. Additionally, Big 4 firms value internship experience. I understand how you might feel that you're not a strong enough candidate, as I had those same doubts, as I went to a smaller school and didn't have any accounting internships, only insurance internships. However, I kept my grades up and I practiced my interview skills, and I was able to land a job with PwC. Keep working hard and it will work out!