You can set up a schedule that is Disabled, then trigger it programmatically with tabcmd runschedule. Individual extracts can be refreshed with tabcmd refreshextract. So typically, people do this by setting up a Windows Scheduled Task that calls a batch file with the tabcmd call in it, and they set it up to run however often they want it to run.

If you know how to write to the Tableau Server db then you could create a schedule then over-write the value in the public.schedules.minute_interval field:

Naturally this is unsupported by Tableau.

I have no idea how to over-write objects in the Postgre db nor how to even get that access