Grant was born and raised in Leonidas, Minnesota. He was the son of an immigrant father who had worked in an open-pit ore mine since he was a young man, and had become a superintendent for U.S. Steel. Grant learned to skate on an ice rink that his father made by flooding a small grassy area near their home. Nicknamed "Cedar Legs" because of his bowed legs, Grant attended nearby Eveleth High School, where he was the left wing and captain of the hockey team that won the first Minnesota state hockey championship in 1945. Eveleth outscored the competition 30-3 in the inaugural tournament. Grant played most of the game in the finals against Thief River Falls and scored the game-tying and game-winning goals within a span of 61 seconds in the third period.