Shotguns are noisy but you aren't gonna shoot them much. Keep the garage doors closed to the extent you can. Shooting from inside it baffles and redirects the noise. Even hanging a few plastic Dollar Store shower curtains around the inside of the garage would probably dampen the noise. Don't shoot before 9AM or after 5PM, and tell the neighbors you've done what you can.
Better yet, invite 'em over to shoot once you're done, show them, tell 'em your plans...