Dawson was born near Mount Davies in the north-west corner of South Australia, around 1935. The exact year is not known, because he was born in the bush and grew up without any contact with Western society. He and his family, who belonged to the Ngaanyatjarra nation, lived a traditional, nomadic way of life in the desert. When he was a boy, Dawson began training as a "" (traditional healer) under his grandfather. He was taught about the country, the spiritual knowledge and law associated with it, and how to use traditional tools and methods to heal people.