One way to do this would be to set a cookie on the splash screen page. Then on your index page you check to see if the cookie is set, if it is not then you should send the user to the splash screen page.
To do this you just need to go to Server Behaviors > Cookies Toolkit > Set Cookie value. Use the before page load trigger, then give it a name and value.
Then on your index page you can add in custom code like this to redirect if this cookie is not set:
<?php
if( !(isset($_COOKIE["<the name of your cookie>"])) ) {
header("Location: <your splash screen page>");
}
?>
You would need to update the name of the cookie to match the one you set, then put in the page where you would like the user to go to.