This could be your problem:

“Whereas a TV receives and processes both video and audio simultaneously from each source, a projector focuses only on the visual elements. Ultimately this means that the projector is unable to process audio and therefore won’t have an audio output for you to connect directly to your Sonos TV speaker. 

Instead, the video and audio from your chosen source will need to be split so that your projector and soundbar can reproduce the images and sound respectively. To do this, you will need to use a device called an HDMI matrix switch. These are also sometimes known as an HDMI switcher.”

https://www.smarthomesounds.co.uk/blog/faqs/how-to-connect-a-sonos-soundbar-to-a-projector

What audio codec is the Chromecast sending? Needs to be DD 5.1 and not DTS or DD+.

Thanks both of you. 

I’ve ended up buying a hdmi splitter and an Amazon Fire Stick 4k. 

The setup goes like this. Fire Stick into HDM In.

HDMI out goes to Optoma. SPDIF out goes to the Sonos Optical Adapter and ultimately goes to Sonos Beam.

For the record, this is Optoma.

And this is Sonos Beam

No luck with this setup, unfortunately. @controlav about `What audio codec is the Chromecast sending? Needs to be DD 5.1 and not DTS or DD+.` As now I’m using a Fire Stick I could see this: https://developer.amazon.com/docs/fire-tv/device-specifications-fire-tv-stick.html

• Dolby Atmos (EC3_JOC). Up to 48kHz, 8 channels, 16-bit and 24-bit

Is Dolby Atmos supposed to work with this setup? Does this have to do with the app that I use from within the Fire Stick? e.g would it make a difference using Kodi or Plex instead of Netflix there?

That codec will not work over optical. You need to select “AC3 (Dolby Digital)”, also listed on that page.

I don’t know enough about the Fire TV but I would expect matching settings changes would be required in each app.

Based on the picture of the Optoma (it as optical output), you should be able to return the splitter once you have configured the Fire correctly and got that working.