How to connect my Apple TV 4K to surround system without optical audio input?!

Play audio in Dolby Atmos or surround sound on your Apple TV - Apple Support

Adjust video and audio settings on Apple TV - Apple Support

• As noted above, you can probably do audio passthrough via the TV. Apple TV → TV → audio system.
• Or you could use an HDMI Audio Extractor Box, to bring an optical output in the setup that way.
• Modern audio receivers will accept HDMI-in for audio, or even allow hub functionality with video passthrough to a TV. Apple TV → TV → receiver via ARC, or Apple TV → AV receiver → TV (all HDMI).

I don’t know which system you have, but I have a couple of ideas for a workaround.

use your tv as the “hub”, connect both surround system and ATV4 to TV, and the surround system should play whatever sound is shown on your tv.

Buy a Bluetooth dongle and connect to surround system and connect ATV4 to it via BT.

Does your surround system accept HDMI? If so, and you have in/out HDMI, you connect ATV via hdmi to the surround system, and from surround system to tv.