If using a cPanel / Plesk type of provider, no there's not a lot you can do since the database server may be set up in such a way that it's on a completely different cluster or machine.
You could automate the install by creating the tables, but not the database and user. You need that in order to connect to the database server initially.
Not to mention that control panels like Plesk and cPanel do extra things when creating databases via their control panel that you can't easily recreate in your installer.