Born in Philadelphia, Wolfe has a twin brother and an older brother. As a teenager she learned piano but she only began to study music seriously after taking a musicianship class at the University of Michigan, where she received a B.A. in music and theater as a member of Phi Beta Kappa in 1982. In her early twenties Wolfe wrote music for an all-female theatre troupe. On a trip to New York, she became friends with composition students Michael Gordon and David Lang, both of whom had recently attended the Yale School of Music and who encouraged her to apply. She went to Yale in 1984 and studied primarily with Martin Bresnick, and she married Michael Gordon the same year. After receiving her M.M. in 1986, Wolfe, Gordon, and Lang founded the new music collective Bang on a Can in 1987.