Typically all deliveries should be scheduled with the super and/or management.
This provides the employee the chance to protect the elevator and make provision for the delivery if need be.
In addition, the delivery company should provide an insurance certificate to management.
If damage occurs, then the negligent party will be held responsible, the maintenance assessed for damages and/or the delivery company’s insurance.
The exact protocol of each building would be specific to the needs and character of the building, but it should always be written in the house rules or somewhere that it can be accessed and read by all residents.

Best
~AR