Finch grew up in East Hampton, New York, and entered the United States Air Force in July 1974. His background was in missile maintenance and professional military education and he served in a number of operational, maintenance, and support units at every level of command, from squadron through Major Command. His assignments included bases in Colorado, Florida, Alabama, Texas, Virginia, and Washington, D.C.. He served overseas in the United Kingdom and Alaska. Finch served as the Command Chief Master Sergeant for the 11th Air Force and Air Combat Command (ACC). While at ACC, the command was involved in operations such as Operation Provide Promise, Operation Northern Watch, Operation Southern Watch, Operation Deliberate Force, Operation Joint Endeavor, Operation Desert Fox, and Operation Allied Force.