Aleksandr Yefremov was born in Moscow in 1904 into the family of a factory worker. In 1916, he began to work as a mechanic helper, later on becoming a mechanic proper at a railway shop. In 1924, he joined the Russian Communist Party (Bolsheviks).
In 1935, he graduated from the STANKIN and worked as a shop foreman, shop superintendent, and then finally as a director of a machine-tool factory named after Sergo Ordzhonikidze. In 1938–1939, Aleksandr Yefremov held the posts of a deputy chairman of the Moscow City Council and then chairman of the Moscow Oblast Executive Committee and chairman of the Moscow City Council. Yefremov contributed to the construction of the third stage of the Moscow Metro and All-Union Agricultural Exhibition. In 1939, he became a member of the Central Committee of the VKP(b).