 Raised in Brooklyn, New York in a traditional, observant Jewish family, Neiman studied in a Yeshiva elementary school, attended public high school and enrolled in City College of New York in 1938

In 1942, he returned to Yeshivah to study Talmud and Rabbinic literature and received Rabbinical ordination in 1945.Following his ordination, he entered the Oriental institute of the University of Chicago, at the time the world's leading institution of Near Eastern studies.In 1950 he received his MA after writing a research thesis on the Letters of Lachish—a set of ancient Hebrew inscriptions, which were discovered in Israel in 1936.