There have been a few posts on how to restore a backup from a Time Machine (or other such backup program).
Within the forum’s posts to date I haven’t seen a solution. But there is one here:
To restore a Local site’s database and files from backup:—
The workflow is to create a ZIP of the backup site’s folders and files, and then import the ZIP as a new site via import.
The website.zip will then contain app, conf, logs, local-site.json.
This is necessary because a simple restore-override of existing website files (app/public) or database (app/sql) will not work as you would expect in version 6.7. Local backs up to app/sql/local.sql on site stop and restart events only. It ∗doesn’t restore from this location on start∗, meaning the only way to get it to ‘import’ the state of a database is the Import ZIP method above.