Claire Falkenstein was born Claire von Falkenstein on July 22, 1908, in Coos Bay, Oregon, a small logging town on the state's rugged coastline. The youngest of three daughters, she later abandoned the use of “von” in her name and worked professionally as Claire Falkenstein. Her father managed a local sawmill, and the forests and timber industry that surrounded Coos Bay had a lasting influence on her life and artistic development. Depictions of sawmills and lumberjacks were recurring subjects in her early work, while carved wood remained an important material throughout her career.

In 1920, the von Falkenstein family relocated to the San Francisco Bay Area, settling in Oakland, where Claire attended Oakland High School and later the progressive all-girls Anna Head School in Berkeley. Falkenstein enrolled at the University of California, Berkeley, where she studied anthropology, philosophy, and art, and it was through the instruction of artist George Lusk that she first encountered European modernism. The Great Depression devastated the von Falkenstein family, forcing Falkenstein and her sisters to pursue independent lives; before graduating from Berkeley in 1930, Falkenstein secured a teaching position at Anna Head School. On July 14, 1934, she married Richard “Dick” McCarthy, a progressive labor attorney, whom she had met in high school.

Entering the new decade, Falkenstein established herself as an artist, exhibiting at local galleries and institutions including the California Palace of the Legion of Honor, the de Young Memorial Museum, and the San Francisco Museum of Art (now the San Francisco Museum of Modern Art). In 1930, she mounted her first solo exhibition, a presentation of charcoal figure drawings at the East–West Gallery in San Francisco. In the summer of 1933, she studied briefly at Mills College with the European modernist Alexander Archipenko, a visiting instructor alongside László Moholy-Nagy. These studies constituted her only formal training in sculpture.

Like many artists of her generation, Falkenstein found opportunities through the Works Progress Administration’s Federal Art Project (FAP). She produced a lyrical fresco of flowers, Poppy Abstraction (1934), for Piedmont High School in the East Bay, and documented life in the rural mining town of Virginia City, Nevada, through a series of drawings demonstrating emerging modernist sensibilities.

In the 1940s, Falkenstein was elected president of the San Francisco Society of Women Artists (SFSWA), and under her leadership, the organization launched volunteer workshops for war agencies and occupational therapy wards. She painted murals in support of the war effort, completing major commissions for hospitals, USO hospitality centers, and other military-sponsored buildings.