Hello SusaGail,
Thanks for posting in the Apple Support Communities.
It sounds like you're unable to launch Apple Music with the latest macOS version installed on your Mac mini, right?
If we have that correct, let's give the steps below a try to see if you're able to clear up what may be occurring. You can find additional information related to what you're experiencing in the following resource to try, if you'd like: Prevent apps and windows from reopening on Mac - Apple Support
Other solutions
• Press and hold the Shift key while opening the app. This doesn't change any settings, but the app forgets any windows that were open the last time you quit the app.
• Make sure that the app isn't a login item. Login items open every time you log in or start up your Mac. You can add or remove login items.
If you're still unable to open the Music app while holding the Shift key, let us know if this continues to happen in another user account on your Mac. If you don't have another user account set up, you can create a test user account to isolate this. We'll be able to gain a better understanding of what could be occurring if you're able to test this out. Check out the following resource for assistance with setting up new users on your Mac mini: Change Users & Groups settings on Mac - Apple Support
We hope that's able to help. If not, provide us with an update and any additional information that you think may be helpful.
Have a great day!