Orenburg Governorate
Yevstigneyev was born into a Russian peasant family on in the village of Khokhly, Chelyabinsky Uyezd, Orenburg Governorate, in what is now the Shumikhinsky District of Kurgan Oblast, in Russia's trans-Urals. He completed seven grades of schooling in 1935 before moving on to vocational school. He trained as a fitter-turner and upon graduation in 1936 moved to work at the Chelyabinsk Tractor Plant, where he joined the local aeroclub which he graduated from in 1938.