Moskvitelev was born into a working-class family on 27 July 1926 in Vyazovy Gai, then part of , Samara Governorate, in the Russian SFSR, USSR. His family was affected by the famines in the early 1930s which caused considerable hardship in the Volga region in which they lived. Moskvitelev's mother died in 1938, while his father took employment as a mechanic at a machine tractor station, but still struggled to make a living wage. After the Axis invasion of the Soviet Union, embroiling the USSR in the Second World War, and reaching the age for service in 1943, Moskvitelev appeared before the authorities and requested a posting to the front. He was instead offered to be trained as a pilot at the 1st School of Naval Pilots in Kuybyshev, which he accepted. He was initially trained on the U-2 and UT-2 aircraft, and in late 1944 was transferred to the . The war ended before he could fly in combat, and his graduation was deferred while the cadets were tasked with helping rebuild the damaged city of Yeysk. Flying lessons resumed in 1946, and Moskvitelev finally graduated in 1947.