Suspension dampers make noise, and pivots creak. Derailleurs and chain tensioners make noise. Disc brakes make noise. Most freewheels and cassettes make noise when you coast.
If you want a very quiet bike, use a single speed coaster brake (crazy cheap) or an Onyx sprag clutch cassette hub (crazy expensive). Use smooth treaded tires (not too fat) but no suspension components--rigid fork and rigid frame. Get a direct drive front hub, like Leaf 1500W or Grin RH212. Mate it with an FOC controller.
"One by" gears with a clutched rear derailleur will prevent front derailleur scraping and substantially reduce chain slap on the frame, eliminating other sources of noise. The shifts are louder and clunkier, though. If you use disc brakes, organic pads are quieter than metallic pads, but they don't last as long.
Then there's maintenance. If you need a quiet bike, you'll have to keep the chain and other moving parts lubricated do they don't squeak, and keep the bearings adjusted to the correct tension so they don't knock or rattle. Use a saddle without springs or any metal parts other than the rails.
With a little restraint and ingenuity, you can have a bike that's maybe even quieter than walking.
If you're only looking to have a quiet motor drive (rather than an entirely quiet bike) so you can use trails where e-bikes are prohibited, well that's another problem that has an easier solution: Don't do it.