Welcome to the forum.
You find yourself in a difficult position as no assembly line documentation exists for any Ford (Mustang included) built prior to the 1967 model year. There is no way to prove that your car is a GT, but many ways exist to prove that it is not.
Example: for the dual exhaust mounting bracket used on all 65- and 66 GT Mustangs, a special spacer (crush plate) was installed on the rear of both rear fame rails. The picture is of the drivers side with a lot of references. No crush plate, it's not a GT.
The second part of the bad news is that the earliest known production GT was scheduled to be built in Dearborn on 20 Feb 1965, Metuchen's earliest known was the end of March, 1965. The Dearborn date has also come under a lot of scrutiny by the MCA and others and it may or not be correct.
Metuchin also used buck tags (a metal tag) attached to the radiator support to assist the assembly line to build the right car. PIO was one of the codes used to signal a GT, GT was stamped later on tags. The tag will reflect most of what the door data tag has. Many buck tags were removed by the factory, dealer or owners.
The bottom line is that your car is most likely not a factory GT, so drive it and enjoy.