The first time you deploy using Trellis for a given site, if you navigate to your site’s domain, you’ll see the wp-admin/install.php screen (if you haven’t already imported a DB or installed WP using wp-cli etc):
I just mean that if you have to rebuild the staging server, you’ll probably run into this screen on the next deploy. You could go ahead with the steps on the install screen, then replace the DB by importing your existing DB, if you have one. That’s just one approach.