He was the son of Mária Miller and Dániel Sula/Schula. His parents were Hungarian (at that time the country name was Austria-Hungary or The Austro-Hungarian Empire) immigrants. His father moved to the United States with his family in 1905. When Dániel's parents decided to return to Hungary, he decided to stay behind. He changed his last name to Shula because he thought it sounded more American.