You can't. Same as with any other email provider.

“Not your keys not your coins” also apply to email. So think about it as a custodial email account. Whenever you use en email provider, you trade privacy for comfort and anonymity (in this case).

It's a bit better since if you only use it for 2FA, you will know the password, and your anonymous email will only know the one time code. So an evil administrator wouldn't be able to steal your account.

For receiving private emails, the same as with other providers apply, encrypt your emails E2E with GPG or similar. Otherwise the sender's provider and your provider will have access to the contents. This applies even if you self host your own mail server.