A native of Sault Ste. Marie, Michigan, Goetz graduated from Sault Area High School in 1915 and went on to study medicine and play football at the University of Michigan. Goetz played varsity football at Michigan for four years from 1917 to 1920. He started nine games as a left end in his freshman year and moved to the left tackle position in his sophomore, junior and senior years. Goetz was also elected president of the University of Michigan Student Council in 1920 and attended the Midwest Student Conference as a Michigan delegate in April 1922.