When you configure CCC to back up your startup disk directly to a locally-attached backup volume, that backup is automatically compatible with Migration Assistant. Occasionally people get into this sticky situation though -- "I have a backup of everything in a folder on the backup volume, I have a clean installation of macOS, now how do I get everything back to the way that it was before?"
This situation requires an intermediary restore to a new, empty volume.
Add a volume to your current startup disk
- Open Disk Utility and select the Macintosh HD volume.
- Click the + button in the toolbar.
- Name the new volume something like Macintosh HD Restore (you can rename this later)
Restore your backup to the new volume
- Open CCC and click Restore in the toolbar to create a new Restore task.
- Drag the folder that contains the complete backup of your previous startup disk onto CCC's Source selector.
- Select the new Macintosh HD Restore volume as the destination.
- Click the Start button.
Install macOS onto the new volume
- Boot your Mac while holding down Command+R (Intel Macs) or the Power button (Apple Silicon Macs) to boot into Recovery Mode.
- Select the Reinstall macOS option and proceed to install macOS onto the Macintosh HD Restore volume.
When the installation is complete, you should be able to log in to your restored account, which was adopted by the macOS Installer.
- Open Disk Utility
- Select the Macintosh HD volume in the sidebar.
- Click the - button in the toolbar. When prompted, choose the Delete Volume Group button.
- Right-click on Macintosh HD Restore and choose the option to rename it; rename it to Macintosh HD.
Reconfigure your backup strategy to create a Migration Assistant-compatible backup
Finally, make a new backup of your startup disk directly to the root of a locally-attached backup disk so you'll have a Migration Assistant-compatible backup from here forward. If you have other data on that backup disk that you want to leave in place, add a new volume to the backup disk for your CCC backup.