Is there a way to make AirPods connect to AppleTV without having to go deep into AppleTV's menus?
Usually (sometimes I do have to go deep into the menu’s) you should be able to swipe down from the top, using your Apple TV remote (works in most apps - not all), and then select your audio device by selecting the “Audio” tab, going down to “Speaker”, and selecting your Bluetooth device.

Alternatively, you can hold the “play/pause” button on your remote when in the “TV” or “Menu” views and select the audio output in a pop up menu.

Related answer (my own) about how to use AirPods easily with multiple devices.