As far as settings within ExpressionEngine go, you cannot do this; EE needs the index.php file (or whatever you’ve renamed it) in order to display your site.

However, if you are on an Apache-based webserver with “mod_rewrite” enabled, then you might be able to use rewrite commands in a .htaccess file to accomplish this.  This article on the EE Wiki discusses how to accomplish this.

Please note that this is a use at your own risk situation.  We do not endorse or provide support for any of these methods.  Other people have reported success, so it’s likely that you can get this to work but it is up to you to do so.