In injury, how soon can a nose be reset if cartilage shifts off bone?

Yes the cartilage needs to be repaired as soon as possible to avoid it healing in the wrong place. Repairing cartilage within 1-2 weeks of injury is ideal. After 2-3 months it's set and becomes surrounded by scar tissue. This make surgery more difficult. However if you find a good nose surgeon with excellent reviews, this can be corrected despite its complexity. 

Dear basscleftonesAfter a fracture, the nose can be reduced to original position, ideally immediately (before swelling) or day5-7 when swelling has subsided and bones have not had a chance to heal. After that window, you generally want to wait at least 6 weeks to try and reduce the fracture, however, in my opinion, 3 months is significantly better. At 3 months or later, all components, including bone and cartilage, can be appropriately repositioned to achieve a good outcome.

The nose can be repaired at any time after an injury to the nose. Trauma to the nose can cause a displaced, or a non displaced nasal fracture. The upper lateral cartilages could also be fractured and displaced off of the nasal bones. To repair a displaced nasal fracture, osteotomies are required  to be placed in the nasal bones.  When the upper lateral cartilages are displaced inward from trauma, a cartilaginous spreader graft is placed underneath it to put it back into its normal position.  A closed rhinoplasty approach can accomplish straightening and repairing the nose with all incisions placed on the inside of it. For many examples, please see the video and the link below