The first Mustang was produced on March 9, 1964. The first Mustang was introduced to the public on April 17, 1964 at the New York World' fair. So, as far as the anniversary date, then yes, March 9 would be the anniversary date.
The First Mustang (s/n 0000001) was a Wimbleton White 64 1/2 convertible sold , by mistake, to Capt. Stanley Tucker , an airline pilot, in St Johns', Newfoundland, Canada. It was a promotional car sent by Ford around the country to promote the new Mustang car. The salesman there, thought the car was to be sold and then did so when Capt Tucker showed interest in the car. It took 2 yrs for Ford to get the car back , in exchange for a new 1967 fastback Mustang (1,000,000,001th ). The '64 1/2 now resides in the Ford museum, still displaying the Nfld and Labrador license plates.