Domb was born on 9 December 1920, the fourth day of Hanukkah, in North London to a Hasidic Jewish family. His father, Yoel, who had shortened his name from Dombrowski to Domb, was a native of Warsaw, while his mother, Sarah, was from Oświęcim, Poland. He was given the Hebrew name of Yechiel. His father and grandfather paid for tutors to educate him in classical Jewish studies, and he also attended shiurim (Torah classes) given by Rabbi Eliyahu Eliezer Dessler to young men in a nearby synagogue.