I am currently working on a new project where the entire page should be implemented in HTML5/JS working against an API/JSON. Since the entire application should only consist of
In case you have your own domain that point at the CDN (I know CloudFront let you do that), you could use CloudFlare ( https://www.cloudflare.com/ ) as a reverse proxy between your users and the CDN.
Thanks to their free plan, you can create a rule that redirects everything to index.html. I think this is the only way to achieve what you want, given that CDNs are configured to serve only static existing files as you know.