Setting index.php as a static home page without posts?

I think you are confuse with templates from pages and posts. Please take a look at Template Hierarchy first. Both home.php and index.php in WordPress are templates. If you need a static page, create a Page instead a Post, and you can name it anything you want, the name is simply a slug, so you can call it Index or Home. Pages can be added into the Menu, and you can specify which one will be your Home (or what you means as the index.php) that will be shown up when you pointing your url to www.your-domain.com.