Even if you could have easily achieved this, the audio would have ‘likely’ been out of lip-sync with the video on screen anyway as the Sonos audio is buffered for device grouping purposes and there’s no way to get around that.
 

You would need one of the Sonos Home Theatre products connected to the PC to get the audio out in a timely manner. The fact you have no Bluetooth or Airplay options with your chosen type of device, is limiting other possibilities too.
 

It’s not what the Play:3 was ever designed to do (sorry about that by the way.)

Perhaps see if there is a third-party solution in the Windows App Store … here’s a link to perhaps help get you started:

https://noxapp.xyz/sonostube-sonos-youtube-app-review-best-apps-for-windows-10/

Please note... I’m not associated with such Apps and I know very little about them, so the risk of using them is entirely your own.

Sorry, bottom line is you bought the wrong speaker for your needs. Best sell it and buy a Bluetooth speaker.