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 [deprecated] 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_carnation