Messenger was born in the Sydney waterfront suburb of Balmain, New South Wales, and grew up in another of Sydney's waterfront suburbs, Double Bay, where his father, Charles Amos Messenger, a champion sculler, owned a boat shed. He also spent some time living with an aunt in South Melbourne, Victoria where he attended the Albert Park Public School. It was there he recalled playing Victorian rules football. He credited skills he learned at Albert Park as contributing to his later success at Rugby Union and Rugby League. Dally was one of eight children. His younger brother by seven years, Walter (Wally) also became an Australian representative footballer.