Shearer was born December 23, 1943, in Los Angeles, the son of Dora, a bookkeeper, and Mack Shearer. His parents were Jewish immigrants from Austria and Poland. Starting when Shearer was four years old, he had a piano teacher whose daughter worked as a child actress. The piano teacher later decided to make a career change and become a children's agent, since she knew people in the business through her daughter's work. The teacher asked Shearer's parents for permission to take him to an audition. Several months later, she called Shearer's parents and told them that she had gotten Shearer an audition for the radio show "The Jack Benny Program". Shearer received the role when he was seven years old. He described Jack Benny as "very warm and approachable ... He was a guy who dug the idea of other people on the show getting laughs, which sort of spoiled me for other people in comedy." Shearer said in an interview that one person who took him "under his wing" and was one of his best friends during his early days in show business was voice actor Mel Blanc, who voiced many animated characters, including Bugs Bunny, Daffy Duck and Barney Rubble. Shearer made his film debut in the film "Abbott and Costello Go to Mars" (1953), in which he had a small part, and appeared in "The Robe" (also 1953). Throughout his childhood and teenage years he worked in television, film, and radio. In 1957, Shearer played the precursor to the Eddie Haskell character in the pilot episode of the television series "Leave It to Beaver". After the filming, Shearer's parents said they did not want him to be a regular in a series. Instead they wanted him to just do occasional work so that he could have a normal childhood. Shearer and his parents made the decision not to accept the role in the series if it was picked up by a television network.