Password

What is your model Apple TV? Identify your Apple TV model - Apple Support

If you have an Apple TV (2nd or 3rd generation), and also two-factor authentication for your Apple ID, then the sign-in procedure is a bit special: Type your password followed by the six-digit verification code directly into the password field.

There is a time limit before the code expires, so it is best to manually request a new verification code after entering the characters of your password, to use those precious seconds effectively for just the code.

Please read the above instructions again. Ignore the code that is send initially, and request a new code at the last possible moment. Then append that code to the password. This way the time limit only applies to the last part, and it should work just fine, as it has done for many other users.