When the system needs to recover from the system state backup, it needs to be done via Directory Services Restore Mode (DSRM).
The first system needs to be rebooted; press the F8 key and select Directory Services Restore Mode.
Once it's loaded to safe mode, we can use the following command:
$ADBackup = Get-WBBackupSet | select -Last 1
Start-WBSystemStateRecovery -BackupSet $ADBackup
This will restore the last backup the system has taken.
If you are using the Active Directory backup software other than Windows, the recovery options will be different from the aforementioned options and refer to vendor guidlines.