Song was born in South Korea. Her parents, both artists, moved the family to Markham, Ontario, Canada when she was 12. Her father, Song Neung-han, is a filmmaker. She has hinted at her Western name being a reference to the character in Celine and Julie Go Boating (1974) directed by Jacques Rivette.
Song wrote her first play, an adaptation of Prometheus, at a classics conference she attended (the Ontario Student Classics Conference) with the Markham District Classics Club.
Song attended Queen's University in Ontario for her undergraduate degree and studied psychology with a minor in philosophy, before receiving her MFA in playwriting from Columbia University in New York in 2014.