There's no way to have S3 ignore the path and just return the root file (index.html). The closest thing to that would be to use an error file that catches all the requests, but although that would load your HTML file, it would always return a 404 status.
You could use URL parameters for paths instead of hashes if you don't want to use those, like this:
www.yoursite.com/?folder/page.html
This would result in the index file of your site being loaded in the browser.