i see the subdomains content.... which is a folder on the root level
You see example.com/sub?
Do you get to choose the directory? If you can try setting it to / or leaving it empty. If you can't you should ask your host about it, suggesting that they could set up a Symbolic link.
To do this with mod_rewrite would require mod_proxy and would be inefficient compared to setting the sub domain's document root correctly or a symbolic link.