I think that what you want to do is to have a php file called index.php that serves your content and a URL that's separate from that.
In App Engine, you actually don't need to do anything special to achieve that effect. When you're going through the App Engine tutorial (https://developers.google.com/appengine/docs/php/gettingstarted/helloworld), you'll notice that the app.yaml file lets you configure which URLs are mapped to which files. In that example, all URLs are mapped to helloworld.php:
handlers:
- url: /.*
script: helloworld.php
But you could also make it so that a specific URL map to a specific php file. For your example of routing domain.com/index to index.php:
handlers:
- url: /index
script: index.php