It seems Tesla have started to publish the factory gate date for cars on their listings. This tool lets you put in your vin and tells you the dates of nearby car vins to see when they were built/left the factory. If you have the vin but no idea when you might get it, this should at least help tell you roughly when it left the factory - more useful for Europe, Asia etc I guess
Tesla Info: check vin for factory dates.
Tesla Info: check vin for factory dates.