Brogan was born on 23 March 1896 in The Dalles, Oregon. He grew up on a stock ranch near Ashwood. As a young man, he worked on ranches in the area around Ashwood and Antelope, Oregon, and then as a sheep camp tender in the Cascade Mountains near the McKenzie Pass. Brogan served as a signalman in the United States Navy during World War I. After the war, he returned to Oregon to work on his uncle's cattle and sheep ranch. Brogan also wrote a few articles for the Antelope Herald newspaper.