You can’t, PHP doesn’t have knowledge of what the default error document is. Sending a 404 status code does not result in redirecting to any other URL. The body of your PHP document is the body of the page sent. If you want to redirect, then you have to do it the same as you did with Google – write out the path or URL to the page you want to redirect to.
When you redirect you issue a 30# HTTP Status code to another page. Redirect to a non-existent page just forces the client to make 2 request one ending in 404. Why do that when all you need to do is embed the 404 content into the page in question.