Bekirbaev was born on 13 October 1928 in Dnepropetrovsk to a working-class family; his father, a Crimean Tatar, worked in mining, while his mother, a Russian, was a schoolteacher. In 1931 the family moved to Taganrog, where they survived the German occupation from 1941 to 1943. After the city was liberated he attended the Taganrog Aviation Technical School in addition to evening school, which he graduated from in 1946. Due to not living in Crimea and having a Russian mother, he was able to avoid the exile that most other Crimean Tatars faced by "passing". Nonetheless, he did not completely disown his Crimean Tatar origins, choosing to keep his surname and giving his children Crimean Tatar names. Having avoided the special settler system, he was admitted to the Moscow Aviation Institute, which he graduated from in 1952.