Nasukhanova was born in 1939 to a Chechen family in the rural village of Starye Atagi. In 1944 she and her entire family were designated as "traitors" because of their ethnicity and deported along with the rest of the Chechen and Ingush nations. Her family was exiled to the town of Taraz in the Kazakh SSR, where she spent most of her childhood and attended school next to an airfield that led to her developing a passion for aviation. Despite constant reminders that she belonged to a "criminal nationality" and being told by her family that aviation is not a woman's job, she went on to pursue aviation after moving to Alma-Ata in 1955. There she was allowed to do make parachute jumps but not fly aircraft at the local aeroclub; but was only granted permission from the authorities to do so because they expected her to quit immediately. While a parachutist at the aeroclub she had a meeting with decorated women pilots Valentina Grizodubova, Nina Rusakova, and Yevdokiya Bershanskaya, which further increased her desires to become an aircraft pilot.