You could you the Tabcmd feature that comes with Tableau Desktop. Creating a batch file that runs the refreshextract utility, and publishes to the Tableau Server with Windows Task Scheduler.
Creating the TDE file Tableau Data Extract Command-Line Utility
Automate the task
How to use Windows Task Scheduler
Example Tabcmd commands
List of all Tabcmd
Do you have a parallel solution for a Mac?
I guess it would be similar, but just easier for me to follow along since I use a Mac. Our Tableau server is on a Windows box, however.