Very basic way would be to use a scheduled task to launch the browser to the correct URL. (Or you could command line that like:
start chrome
https://live.atheycreek.com (Assuming Chrome is installed, leaving it out will use the default browser.)
Then a separate task designed to trigger after the first to run a VB or Powershell script to run the appropriate keyboard commands.
Alt-Enter is a typical keyboard shortcut for full screen, and unmute should be relatively easy to figure out. VBScript 'SendKeys' command is probably what you are after. Might also need code to focus on the appropriate window.
Camtasia supports some simple command line bat files that can be used to start and stop recording with a scheduled task.
https://support.techsmith.com/hc/en...e-a-Recording-to-Automatically-Start-and-Stop
A much more complicated way would be to write some javascript to launch the browser, navigate to the website, and take the appropriate user actions.
Also automated testing software out there that could be re-purposed for this. As well as other applications that can record use actions and replay them later.