Evans was born on March 22, 1932 in Manhattan, the son of Bella (Shotl) and Harry Evans. His family was Jewish. He learned much about the game by playing for ten cents an hour on 42nd Street in New York City, quickly becoming a rising star. At age 14, he tied for 4th–5th place in the Marshall Chess Club championship. The next year he won it outright, becoming the youngest Marshall champion at that time. He also finished equal second in the U.S. Junior Championship, which led to an article in the September 1947 issue of Chess Review. At 16, he played in the 1948 U.S. Chess Championship, his first, tying for eighth place at 11½–7½. Evans tied with Arthur Bisguier for first place in the U.S. Junior Chess Championship of 1949. By age 18, he had won a New York State championship as well as a gold medal in the Dubrovnik 1950 Chess Olympiad. In the latter, his 90% score (eight wins and two draws) on sixth board tied with Rabar of Yugoslavia for the best result of the entire Olympiad.