On private property, including your own driveway or a fenced site, Mason asks for no container permit. The City's waste chapter is written about collection service rather than about containers on private ground.
The right-of-way is where a permit appears, and Mason names the office plainly. Any work in the city's right-of-way, including on roads, streets, alleys, sidewalks, curbs, gutters or any other paved surface, needs a permit from the City Engineer first, and the same chapter carries a fee, a bond, a restoration duty and a requirement for barriers. That reaches a container set in the street or across the walk.
The sidewalk itself is effectively closed to a standing container. The City's health, safety and sanitation rules allow material on a sidewalk only for the time a delivery or pickup genuinely takes, and in no case for more than one hour, with each day treated as a separate offence. The same section requires sufficient protection over the pavement before heavy material is carried across a sidewalk or curb, so plywood under the wheel path is the practical answer.
One rule here works for you rather than against you. Mason's waste chapter says that where large containers are used, the business contracts with the hauler privately, and it goes further: a commercial establishment averaging more than ten cans a week is required to use a dumpster. If you also want to come off the City's own collection, the City Manager needs proof of your agreement with a private service, which must use covered trucks and match the City's own collection frequency. That last condition is worth raising before you book a long rental, and your account manager will put the question to the City for you. The City Engineer's office handles the right-of-way side.