No, this cannot be done. Replace the tire. You may also need to replace other tires depending on tread depth and whether you have four wheel driv or not.
You can have a professional tire technician remove the tire for inspection / evaluation - however a sidewall injury ‘usually’ means tire repair should not be attempted.
Certainly not by plugging the tire!
RepairPal Certified shops can diagnose and repair your 2011 Chevrolet Avalanche. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.