I think we have some examples for this for WordPress also, but for a Drupal site, there's a new flag for installing a new site from existing config, which could be shipped from a custom upstream.

 --existing-config             Configuration from sync directory
                               should be imported during installation. Use
                               with Drupal 8.6+.

So we could write something like this on deploy_product:

passthru('drush site:install --existing-config');

For WordPress, we have a working example that uses a mix of commands, but would like to have a more consistent framework that doesn't involve storing a db in the upstream.