Use drush site-install command.
Basically you use something like this:
drush site-install openy --account-pass=password --db-url="mysql://user:pass@host:3306/db" --root=/var/www/docroot
Complete YMCA Website Services profile preset and YMCA Website Services Rose theme is used in this case.
You can set which preset must be installed by specifying it with openy_configure_profile.preset variable, and theme with
openy_theme_select.themevariable e.g.:
drush site-install openy --account-pass=password --db-url="mysql://user:pass@host:3306/db" --root=/var/www/docroot openy_configure_profile.preset=extended openy_theme_select.theme=openy_rose