A possible solution to your problem would be to create a new subdirectory under the current website. So i am going to pretend that you have called it "newsite". Now upload all the files to that directory and go to "thecurrentsite.com/newsite" and you should be greeted by the already familiar Silverstripe installer... go ahead and finish the installation as usual.

After that you can go on developing the site and you client should see steady progress as the dev process goes on. When you are done developing and you client is happy here's what you need to do

- Move all the file from the "newsite" folder into the root folder of the website.
- Next, delete or rename the current "index.htm or index.html" file from the old website.This is important because by default Apache web server is configured to serve those files.

- Finally and this is the most important part. Open the ".htaccess" file you moved from the "newsite" folder and edit the following lines

to this

And thats all there is to it. Hope this helps.