Yes, It is possible to study in the U.S without giving your GRE exams. As a matter of fact, here are the top universities in the united states that don't require your GRE scores for you get admission into:
- Columbia University
- Massachusetts Institute of Technology (MIT)
- University of California, Berkeley
- Alabama A&M University
- Central Michigan University
iSchoolConnect's blog(https://ischoolconnect.com/blog/us-schools-without-gre/) has a detailed list of colleges that don't require GRE exams. Do check them out.