Nielsen lived for several years in Fort Norman (now Tulita) in the Northwest Territories, where his father was with the Royal Canadian Mounted Police. His father was an abusive man who beat his wife and sons, and Leslie longed to escape. When he graduated from high school at 17, he joined the Royal Canadian Air Force, though he was legally deaf (he wore hearing aids most of his life). Following graduation from Victoria High School (now called Victoria School of the Arts) in Edmonton, Nielsen enlisted in the Royal Canadian Air Force and trained as an aerial gunner during World War II. He was too young to be fully trained or sent overseas. He worked briefly as a disc jockey at a Calgary, Alberta, radio station, before enrolling at the Lorne Greene Academy of Radio Arts in Toronto. While studying in Toronto, Nielsen received a scholarship to the Neighborhood Playhouse. He noted, "I couldn't refuse, but I must say when you come from the land of the snow goose, the moose, and wool to New York, you're bringing every ton of hayseed and country bumpkin that you packed. As long as I didn't open my mouth, I felt a certain security. But I always thought I was going to be unmasked: 'OK, pack your stuff.' 'Well, what's the matter?' 'We've discovered you have no talent; we're shipping you back to Canada. He moved to New York City for his scholarship, studying theatre and music at the Neighborhood Playhouse, while performing in summer stock theatre. Afterward, he attended the Actors Studio, until his first television appearance in 1950 on an episode of "Studio One", alongside Charlton Heston, for which he was paid $75 ().