Aaron Goldberg was born in Boston to Alfred Goldberg, a biochemist, and Joan Helpern Goldberg, a hematologist, and has one younger sister, Julie Goldberg. He began taking piano lessons at 7, and started playing jazz when he was 14. As a high school student at Milton Academy, Goldberg was introduced to improvisation by Bob Sinicrope, the founder of Milton's Jazz Program, and at 16 studied with saxophonist Jerry Bergonzi. Goldberg moved to New York City at 17 to attend the New School for Jazz and Contemporary Music, and devoted his off-hours to practicing the piano and performing in New York clubs.