You can always install wordpress in a folder and work on it and if you still want to keep it private make it a password protect folder that only you know the password.
so you would have http://domainname.com/folder
I think I’m confused. The only way I’ve ever installed WP is through my hosting company and I always have to do a DNS change before I am able to actually work on the site in WP-admin. However, this time I don’t want to do the DNS change until my site is all done.
Are you maybe talking about installing WP in another way?
You can install wordpress on same domain name no DNS change
Say your client has website on http://domianname.com this website stays as is still live.
Now you go on same host account if he/she has given you login details create a folder in public_html
Install wordpress in that folder and you will work in that folder with wordpress
so you will http://domain name.com/folder for your wordpress and to log in admin you will have http://domain name.com/folder/wp-admin
The present website will still be live.