Coppola grew up as the second-youngest of five children in Long Island, New York. Coppola's lower-income family, headed by a black mother and Italian father, did not fit in, and she and her family were picked on. Her circumstances encouraged her independence and also her creativity, as her family, who received welfare, had little money to pay for entertainment. Her mother, a teacher, was the primary income earner, while her carpenter father was often out of work and refused to earn an income from his art.
Coppola grew up surrounded by music, as her father is a jazz musician, her mother plays bass, and all of her brothers and sisters are musically inclined. She says her first musical memory is of her father, who was her biggest musical influence, playing the song "Bessie's Blues" "on a severely out of tune piano." She began playing violin at the age of six, eventually studying studio composition at the State University of New York at Purchase. She was not happy and left after one year, but during her time at Purchase, she made some demos and passed them on to her older sister Maya, who is a singer-songwriter in the music business. Maya gave them to her boyfriend, music publisher Ross Elliot, who got Coppola together with producer Michael Mangini at Digable Planets. While still in college, Coppola cut three demo tracks with Digable that resulted in a bidding war for the artist among other studios. Coppola accepted a recording contract with Columbia Records in 1997.