Sabur was born in New York City, New York. Her mother, Julie Sabur (born Kessler), worked as a reporter for News12 Long Island until 1995. She married Mohammed Sabur, a Pakistan native, in 1980. Alia, born on February 22, 1989, showed early signs of giftedness. She tested "off the IQ scale," according to an educator who tested her as a first-grader. As a fourth-grader, she left public school and was admitted to Stony Brook University at the age of 10, later graduating "summa cum laude" at 14. She also received a black belt in Tae Kwon Do at the age of 9.