Schlessmann, the son of a locksmith, attended elementary and secondary school in Essen. He left school in 1914 without attaining his diploma and worked as an apprentice locksmith in the Krupp factory until May 1916. He then volunteered for service with the Imperial German Navy in the First World War. He was stationed first in Kiel, then in Wilhelmshaven with the U-boat fleet and assigned to U-100 until discharged after the end of the war in November 1918. In March 1919 he briefly reentered the navy and served as a machinist on a minesweeper until again discharged in May 1919. He returned to work as a locksmith in Heidelberg and Wertheim am Main. He also served with the Freikorps Roßbach in opposing the Ruhr uprising in March 1920. For the next two years, Schlessmann trained as a technician at state mechanical engineering schools in Essen and Elberfeld, passing his engineering examinations in August 1922.