Norwitch was born in Odessa, Russia (present-day Ukraine) in 1894 and emigrated to the United States with his family as a child. Initially settling in Baltimore, Norwitch went to work at a clothing factory from the age of 13. He married Mae Schreiber in about 1917; they had two children, Mildred and Bernard. Norwitch became affiliated with the Amalgamated Clothing Workers union and moved to Philadelphia in 1926 to work as a business agent for the Joint Board Cutters and Trimmers Local 110. His union work brought him into local politics, and he became active in the Nonpartisan League, a socialist group, in 1934. He joined the Democratic Party and served as a delegate to the 1948 Democratic National Convention in Philadelphia, where President Harry S. Truman was nominated for a new term.