Baev was born in Astrakhan in 1875. He was a relative and childhood friend of Mariinsky Theatre singer Nadezhda Papayan. He studied in local gymnasium and then attended the Saint Petersburg Institute of Civil Engineering, from which he graduated in 1901. From 1911 to 1918 he worked as the main architect of Baku. During this period he constructed more than 100 buildings in Baku, including the Great Theatre of the Mailov Brothers (modern days Azerbaijan State Opera Theatre, 1911), Sabunchi Railway Station, a residential sector in the former Armenikend area of Baku, and other buildings.