Two cents here in addition to the advise by @den.thed
This method will WIPE ALL Data and there is No DATA Recovery - Period.
>> Only works on Intel Based Apple Computer <<
To perform this action will require booting from a Bootable Installer.
The Bootable Installer can Only be performed on an Apple Computer
This will have to be performed from a Qualifying Computer to run the version of macOS to be made on the Bootable Installer. Example : Bootable Installer of Big Sur would have to be done on a computer that Qualifies to run Big Sur.
Notation: If the computer being used to perform this action is Too New or Too Old to qualify to run the version of macOS - this computer can’t be used.
Alternative is, to gain access to a Qualifying Apple Computer from a family member, friend or associate.
Shutdown computer and disconnect all external drive Except the newly created Bootable Installer.
Restart and immediately hold the OPTION key until the Startup Manager appears and choose the USB Drive.
It will present options >> Disk Utilities >> View >> View ALL attached Drives.
Choose the Upper Most Drive ( not the volumes indented and list below ).
The drive normally is called Apple Media or Apple SSD - that is the drive to Erase and format as APFS with the GUID Partition Map.
Once that is done >> backup out of Disk Utilities and choose install macOS.
Follow the prompts and it may automatically reboot several time.
Upon a final reboot - Setup Assist will present with the newer version of macOS.
