He was born in Oni, Georgia (then part of the Russian Empire) into the family of the leading Georgian Zionist David Baazov.
In 1925, he organized a Tbilisi-based Georgian-Jewish dramatic troupe "Kadima" and began writing plays depicting the life of the Georgian Jews.
In 1927, he graduated from the Faculty of Law, Tbilisi State University, and briefly served as a lawyer.
Through his 1928 play Dilleamari (დილლეამარი), Baazov established himself as a leading writer in Georgian on Jewish themes.
In an amazingly brief period, Baazov wrote ten plays (notably The Mutes Began to Speak [მუნჯები ალაპარაკდნენ, 1931], Without Respect of Persons [განურჩევლად პიროვნებისა, 1933], Itska Rizhinashvili [იცკა რიჟინაშვილი, 1936], etc.