Elinor Claire Awan was born in Los Angeles, California as the only child of Leah Hopkins, a musician, and Adrian Awan, a set designer. Her parents separated early in her life, and Elinor lived with her mother most of the time. She attended a Protestant church with her mother and often spent weekends with her father's Jewish family. Growing up in the post-Depression era to divorced artisans, Ostrom described herself as a "poor kid." Her major recreational activity was swimming, where she eventually joined a swimming team and swam competitively until she started teaching swimming to earn funds to help put herself through college.