Babayan was born on 15 August 1901 in the village of Zykhchi in Kars Oblast (now in Turkey) to an Armenian peasant family. He graduated from junior high school in 1916. In 1917, he volunteered for the Imperial Russian Army, fighting in the Caucasus Campaign against Turkish troops. After the collapse of the Imperial Army, he joined the army of the Armenian National Council, fighting in the Battle of Sardarabad in late May 1918, during which the Ottoman invasion of Armenia was repulsed. After Sardarabad, the First Republic of Armenia was proclaimed and Babayan joined the new army of the republic, serving with the 2nd Rifle Regiment at Vagharshapat. In May 1920 he deserted and returned to his homeland. After the Soviet occupation of Armenia in on 29 November, Babayan joined the Red Army's Voronovich Special Detachment in the village of Kanaker, later serving as a Red Army man with the 4th Lori Armenian Rifle Regiment. With the regiment, which became part of the 20th Rifle Division of the 11th Army, he fought in battles on the Caucasian Front, in the overthrow of the Democratic Republic of Georgia, and the suppression of the Dashnak revolt in Armenia.