Mine works fine without contacts. Maybe try reinstalling?
Launch app Chats tab is active by default Tap the chat icon lower right side Whatsapp "To help you connect... allow access to your contacts. Not now or continue"
I tap not now, and am returned to Chats and no way to manually enter a number. Tap the chat icon again, same thing.
Android app info for Whatsapp says no permissions.
This is Android 9. Deleting and reinstalling hasn't changed this behavior.