Short answer is NO.
One can not install Big Sur Over Monterey.
To achieve an downgrade will require a good amount of time to preform this. It will also require starting from scratch and reinstall the Big Sur.
If this is an Apple Silicon M1 computer, the below WILL NOT Work and should not be attempted.
This will Wipe ALL Data and there is no recovery - period
To perform this action will require booting from a Bootable Installer.
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.
Once that is done read on for preparing the Destination computer >>
Only works on Intel Based Apple Computers.
Extra Special Notation regarding the Touch ID equipped Apple Computer.
About Startup Security Utility and Must Enable from Recovery Mode the ability to boot from External Drive Before Attempting
1 - Shutdown computer and disconnect all external drive Except the newly created Bootable Installer.
2- Restart and immediately hold the OPTION key until the Startup Manager appears and choose the USB Drive.
3 - It will present options >> Disk Utilities >> View >> View ALL attached Drives.
4 - Choose the Upper Most Drive ( not the volumes indented and list below ).
5 - 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.
6 - Once that is done >> backup out of Disk Utilities and choose install macOS.
7 - Follow the prompts and it may automatically reboot several time.
8 - Upon a final reboot - Setup Assist will present with the newer version of macOS.
