Apple TV 4K

If your audio system has S/PDIF connectivity (optical or coaxial), then you can likely get audio passthrough from the TV:

Apple TV →[HDMI]→ TV →[S/PDIF]→ audio system

When possible, passthrough is likely easier than the use of an HDMI Audio Extractor box.

You may need to set the Apple TV to output Dolby Digital, instead of Auto (PCM Multichannel).

Which exact model sound system (12-II, 20, 25, 28-II, 30-II, 35-III, 35-IV, 38-IV, 48, 48-IV, 50, 535, 600, T10, V35)?

Does it have HDMI-in?

Does it have HDMI-out?