If it happens again then, to help find the ‘culprit’, within 20 minutes of the issue occurring, submit a Sonos diagnostic report from the ‘Settings/Support’ area of the Sonos App. Make a note of the reference generated, and when practicable, contact/chat to Sonos Support Staff about the matter via this LINK and see what device on your network started the playback.

It has been known that pets/small animals can operate a speakers touch controls too, but start with finding the source that caused the speaker to play. 

Hope that then leads to the answers you are looking for here.

There have to this date, not a single case in which this has been a problem with Sonos themselves. In every ‘solved’ case (not everyone reports back) it’s either been something set up as an alarm, either in the Sonos software, or in a third party controller, such as Alexa, HomeKit, etc. The remaining issues have been ‘friends’ with Spotify Connect who forgot to disconnect when they left your WiFi, or the owner disconnecting them by streaming a non Spotify stream on their Sonos system.

If you’re still convinced it is a Sonos issue, submit a diagnostic within 10 minutes of the system starting to play, and call Sonos support. That diagnostic should have data about what initiated the stream and Support would be able to tell you. And if it turns out to be a Sonos error, they’ll have hard data to provide the engineers so that the ‘bug’ can be resolved.

I do not have any of those third party controllers -- it was to avoid those that I got Sonos in the first place. Nor have I had friends over with Spotify.

I have my ARC set to Autoplay the TV. Wednesday night is very risky because this is when the cable company updates the cable box. At the end of the update the cable box turns ON and ARC assumes that I want to watch (and listen) to whatever channel is playing. I have resorted to reducing the ARC Volume to zero when I end a TV session. Or, I can defeat AutoPlay.

If, as you say, you have no explanation, I would encourage you to follow the rest of my suggestion, as I recommended, and submit the diagnostic after it happens. I believe Sonos can see where the command to start play comes from. 

And if, for the first time, it turns out to be an issue with the ever changing Sonos software, please let us know, so that we have knowledge of the initial event.