Alexander was born in Philadelphia on January 30, 1924 to Edna (née Chudley) and Alan Audley Alexander, and grew up in Drexel Hill, Pennsylvania, a section of Upper Darby just west of the city. He had an elder sister, Florence. His parents only read newspapers, but they did buy books "at the Salvation Army to fill up empty shelves." He taught himself to read around age four and skipped grades one and two at a private Quaker school. He and his friends played at war, using equipment from World War I in their games. After his father Alan, a stockbroker, bankrupted in the Wall Street Crash of 1929, Alexander attended public school, where he skipped yet another grade, entering seventh grade at age nine. Alexander read Shakespeare, Dickens, Mark Twain and myths, especially King Arthur. In addition to being interested in art, at age thirteen, Alexander wanted to become an Episcopalian priest; however, his family could not afford to send him to divinity school. Passionate about writing, Alexander believed he could preach and worship God through his writing and his art. In high school, he began writing romantic poetry modeled after the work of nineteenth-century poets and writing narrative short stories, but he failed to acquire interest from publishers. His parents found him a job as a bank messenger, which inspired a satire that would become his first book published fifteen years later, "And Let the Credit Go" (1955). He graduated at age sixteen in 1940 from Upper Darby High School, where he was inducted into the school's Wall of Fame in 1995.