On the radio, the announcer states it's the 62nd Kentucky Derby, which took place on May 2, 1936. However, Fort Knox did not start taking gold shipments until January, 1937.
The driving distance between New York City and Louisville, Kentucky is 737 miles and would take about 12 hours - in 2024 with modern interstate highways. At the time of this film it would be much further driving distance and take a much longer the than depicted - less than an overnight drive.