Westlake was born in Perth, Western Australia, the son of clarinettist Donald Westlake. He attended the Sydney Conservatorium of Music, but left the school early to pursue a professional career in music, studying clarinet with his father. Eventually, he studied at the Australian Film and Television School under William Motzing. In the early years of his career he was a freelance performer and composer, playing throughout Australia and in parts of Europe in recording sessions, chamber music concerts, theatre and ballet performances, as well as tours. He was a member of the Magic Puddin' Band and was later invited to be a part of the Australia Ensemble, a group of musicians that played new Australian classical music.