I think this timeline from the Michigan Wildlife Conservancy says it all:
MILESTONES IN THE HISTORY OF COUGARS IN MICHIGAN
Pre-Settlement – Cougars are indigenous to all 83 counties of Michigan.
1830 – 1930 – Cougars and other predators are hunted and trapped by the government and citizens to accommodate the expanding human population.
1907 – The Sault St. Marie Evening News reports on a five-foot six-inch, 80-pound male cougar killed in a wolf trap near the Tahquamenon River in Chippewa County.
1914 – 1922 – N.A. Wood of the University of Michigan Museum summarizes historical accounts of cougars in both the Upper and Lower Peninsula. The Michigan Conservation Department begins to list cougars among predators vanished from the state.