Why will the car not take gear until it warms up for approximately 20 minutes?

Hello, if there is no engagement for the transmission until the engine "warms up" you likely have an internal transmission mechanical concern that will need looked at. Seek a local transmission repair shop or a shop in this list for help: https://repairpal.com/repair-shops/chevrolet-repair-and-service-in-new-tazewell-tennessee

Recommend regular service: Do not know your skill level .. Remove transmission pan - fluid will drain - replace transmission filter - replace pan with new gasket - refill transmission. Possible restricted filter + contaminated fluid - fluid is not as viscous when warm and will flow more freely through dirty filter.. Do not have transmission flushed!