Be sure you have a minimum of 35.5 GB of free space available for installing Big Sur. More, much more if possible - like 80+ GB which will also improve general overall performance.
If you current attempt isn't successful try the following:
1 - boot into Safe Mode according to Start up your Mac in safe mode - Apple Support .
NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following;
• Verifies your startup disk and attempts to repair directory issues, if needed
• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)
• Prevents Startup Items and Login Items from opening automatically
• Disables user-installed fonts
• Deletes font caches, kernel cache, and other system cache files
2 - go to the App Store, search for Big Sur and download the full sized installer.
3 - run the installer from the Safe mode.