You can’t send audio from the ATV to your Connect:Amp over the network. The C:A would need to input the audio via its analog Line-In jacks. However note that Line-In incurs a 75ms (minimum) delay so if you need to synchronise audio with video then lip-sync could be affected.
As for the analog signal it could either come from whatever the ATV is feeding over HDMI (if there’s such an output on the TV etc) or using an HDMI audio extractor device inserted into the cable. The ATV would need to be configured to output PCM stereo, not Dolby surround.
Keep an eye on that Bridge, they are obsolete and prone to hard to diagnose issues. Often a failing power supply.
You probably don’t need it anyway as you should be able to connect your Connect Amp to your WiFi and have better results.
https://support.sonos.com/en-us/article/switch-sonos-between-a-wireless-and-wired-setup
Thanks for the information guys.