Under Edit Game: At the very bottom of the page, select Draft
The creator can do anything they want to the game, the upload, the display page, but nobody else except the creator account has access to it. Unless…
If you go to the game page, it will show Draft at the top. If you click Secret URL the URL in your browser will be extra long and difficult and persistent, so you can share this privately with your testers who can link to the game and/or downloads as a normal user (they do not need to be registered on itch.) You can even use the forum and feedback on the page, though I think that requires any posters to have an itch account.
There are other more complicated access features. Controlling who can access your project - itch.io
Be aware that the “Secret” URL gives access to anyone who can click it, so if you’re wanting to keep your game unpublished for a Comp, you won’t want to post the Secret URL publicly. You can also select to protect your Draft game with a password or give out access keys for extra security.
When you move the game into “Public” mode then it is searchable on itch and the Secret URL will redirect to the main game page…but you don’t ever have to make it public if you just want to use itch for beta-test distribution.