Upon completing her studies at the Academy, Gobbi was contracted with the National Theater in 1935 and began participating in many productions. She was a featured artist in the productions of the Vasas Trade Union. Gobbi's first film role was in "The Borrowed Castle" (, 1937) and the following year, she filmed "The Lady Is a Bit Cracked" (, 1938), in which she played an eccentric madwoman. Even in her younger days as an actress, Gobbi earned her reputation by playing older women. During the Nazi occupation of Hungary, Gobbi worked with the Resistance. Her father created forged documents to exempt men from military service, which Gobbi distributed.