unless you have deployed an app.yaml file that is different from the tutorial (as described
here), you probably just forgot to deploy the static file index.html into your app's www/ directory as described
here. Also for this tutorial example, the www/ directory should be in the same directory as your app.yaml file. For example:
/my-local-computer/my-app/
/my-local-computer/my-app/app.yaml
/my-local-computer/my-app/www/index.html
/my-local-computer/my-app/www/css/style.css
and so on.
According to the error page, the request actually reached your application, so you will be able to investigate the requests in your logs.
In Cloud Console, go to Logging, select your App Engine project (so you can see the logging for all services of the app), and search for a request that caused this 404 status and the path "/". Optionally, you can enter "status:404" in Logging's text search to filter for such logs.
Expand a matching log record and you will see details that probably will tell you what exactly went wrong under the hood. The user-facing error pages are not very helpful for debugging (and they shouldn't be for security reasons).