Walsh was born in Sydney, New South Wales, the son of Michael and Mary Walsh. He grew up in the western suburb of Werrington, where his father owned a dairy farm. He was educated at St Joseph's Convent School and later at Parramatta High School in the Sydney suburb of Parramatta. In 1926, he won the T E Rofe Prize, worth £6, for the best history essay in the state, writing on the Mutiny on the "Bounty".