Honestly, I believe that more than the institute it is your caliber and dedication level that decides if you will be able to crack USMLE. The AIIMS tag definitely helps but is not the sole medium through which you can crack USMLE.
Here is a shining example that proves my theory. Dr. Nikhil Munshi neither did his MBBS from any AIIMS nor a Delhi college yet managed to crack USMLE. He completed his medical degree from Maharaja Sayajirao University, followed by an internship and residency in internal medicine at Shri Sayaji General Hospital and Maharaja University in India. After completing an oncology fellowship at Johns Hopkins Oncology Center, he became a professor of medicine in the Department of Medicine at Harvard Medical School, as well as an attending physician at VA Boston Healthcare System and Dana-Farber Cancer Institute. His journey proved that even an average college can produce excellent doctors and vice versa. What you should focus on is yourself and not the institute.
So we can say that studying at AIIMS or Delhi colleges like MAMC gives you an upper hand at USMLE for sure but are not necessary for the same.