There is a way in a PowerShell script to check if QAP is running and, if necessary, launch it.
See
https://www.google.com/search?q=powershe...is+running
Then, in the script open the menu with run
"C:\Program Files\Quick Access Popup\QAPmessenger.exe" ShowMenuLaunch
But, as Horst mentioned, it is simpler to have QAP always launched at Windows startup.