Dear Mr. Shewmake,
Thank you for posting your request on History Hub!
Because driver licences were issued by states, we suggest that you contact the State Archives for the state you are researching to inquire as to the disposition of driver licence records from this time period. Individual state archives should be able to let you know if licence records were created by their states for this time period, if they still exist, and if they can be accessed.
Please note that not all states started issuing licences at the same time, and some did not introduce them until the 1950s. Please see the following article: https://www.history.com/news/when-was-the-first-u-s-drivers-license-issued
We hope this is helpful. Best of luck with your research!