Their appears to be a sales contract with the salesman name of Harding shown. The date on the contract is April 15, 1964. I don't think anyone has posted a earlier date.
I saw that in the video too.
One question remains that though the sales slip shows April 15, 1964 and Gail even quotes the day of the week (Wednesday) she first saw
and bought the car, but what was the actual DELIVERY date? It doesn't change when it was bought, I just wondered when it was first driven off the lot or publically seen on the road. I believe nobody claims the actual delivery date in the video, or the day driven off the lot as April 15th. That was my take-away of the video.
It seems reasonable to believe that they didn't walk into the showroom with "cash" or that a personal check payment would allow just anybody to drive away a new car on the spot. More reasonable to believe the dealership would wait till somebody took the check to the bank and to have it clear. (next day or two)