Sandra Day was born on March 26, 1930, in El Paso, Texas, the daughter of Harry Alfred Day, a rancher, and Ada Mae (Wilkey). She grew up on a 198,000-acre cattle ranch near Duncan, Arizona. The ranch was nine miles from the nearest paved road. The family home did not have running water or electricity until Sandra was seven years old. She hunted from a young age, using a .22-caliber rifle to shoot jackrabbits for food. She began driving as soon as she could see over the dashboard and had to learn to change flat automobile tires herself.
Sandra had two younger siblings, a sister and a brother, respectively eight and ten years her junior. Her sister was Ann Day, who served in the Arizona Legislature. She later wrote a book with her brother, H. Alan Day, Lazy B: Growing up on a Cattle Ranch in the American West (2002), about her childhood experiences on the ranch.