Under Release status, select In development, as you'll probably want to get beta testers and make further changes. You can change this to Released prior to submission.
Under Visibility & access, select Restricted, then additionally select Also allow a password to view page and enter a password. You can change this to Public prior to submission.
If you follow these steps, it will never be listed by itch.io and if someone happens to stumble upon your page, they can't run the game or do any downloads unless they know the password. You can give the password to your beta testers.
There's no hurry to submit your game until it's getting close to the deadline.