Born in Westchester County, New York, to a Jewish family, Hammer grew up attending what he described as a "fairly Reform" synagogue. However, over time, he embraced Orthodox Judaism, marking a significant shift in his personal and spiritual journey. This evolution would later inform much of his worldview and public advocacy.

Hammer graduated from Duke University in 2011 with a Bachelor of Science degree in Economics. During his undergraduate years, he developed a keen interest in economics and policy, which led him to work in antitrust research after graduation. Seeking to deepen his expertise in law, Hammer attended the University of Chicago Law School, where he earned his Juris Doctor in 2016. While there, he became actively involved in conservative intellectual circles, including the Federalist Society and the Edmund Burke Society. He also served as a fellow at both the Claremont Institute and the James Wilson Institute, institutions renowned for their focus on constitutional principles and natural law.