If i understand correctly then the following is a good way to do this.
1) Build the new site under another unused url on a live production server at your hosting company (this can be any url whatsoever)
2) Once the site is finished then you need to do a ‘domain mapping’ . This points your unused url (i.e the one you used to build the site on ) to the live url.
Let me know if this makes sense :)