Esch was born and brought up in Memel (Klaipėda). In late 1944 he was evacuated to Mecklenburg, where he was drafted into military service as a Navy–Flakhelfer. In 1946 Esch started to study law at the University of Rostock and became a member of the Liberal Democratic Party of Germany (LDPD). He opposed against the claimed leading role of the communist Youth organisation Freie Deutsche Jugend and was elected into the LDPD committee in 1948 and the LDPD executive committee in 1949. He was a co-author of the "Eisenacher program" of the LDPD.