After graduating from Israel's Alon School of the Arts in 2007, Levy began her military service as a singer for the IDF Musical Ensemble.

Following the completion of her military service in 2009, Sivan was cast in her first film, Burning Mooki, directed by Lena and Slava Chaplin.

Levy began working in television in 2009, when she joined the cast of the renowned primetime TV series Ima'lle [he] on Channel 2, directed by Ram Nehari.

Later that year she appeared in Room Service, directed by Eitan Aner, and in 2010, Sivan reunited with directors Lena and Slava Chaplin, starring in the Israeli TV film In the Prime of Her Life, a modern adaptation of the works of Israeli author Shai Agnon.

Water Wells (2010), for which she composed an entirely original soundtrack, received worldwide festival exposure including Sundance's 'Outfest'.