installed WP on live site but want to keep current as is until I customise theme

Hi Folks,
I just installed WP on an old site I have hosted. This old site is currently due to get a WP makeover 🙂

The original htm files are all live and this is ok as I want to work on the theme and then when it is ready delete the old htm site files.
problem: if “mysite.com” is entered in browser they WP theme is displayed- dont really want this in public view.
if “www.mysite.com” is entered in browser then the current site is shown this is good (whilst i work on the theme in the background)

is there anything that can be done so that the WP is not appearing this easily.
needless to say I am only new to WP

thanks