2 options as I see it:
1) Remove the stuff in the public_html (root) and move the joomla site to it, or
2) Redirect subdiretory to the root as described below.
Here is what I do...
1) Build your joomla site in a subdirectory
2) Log in to cpanel
3 Go to Redirects section
4) In "Add Redirect´s first field enter the subdirectory, so it says http://yourtchdomain.com/subdirectorysname
5) In the other field, enter yourtchdomain.com
6) Choose if the redirect is temporary or permanent and click add.
7) Now when people go to yourtchdomain.com, they will be redirected to yourtchdomain.com/subdirectorysname and you canclean your root without people seeing it and eventually if you want you can remove the redirect and move the joomla installation to the root.
If things doesn´t become what you want, you can always delete the redirect.