I don’t own a google home hub and don’t know much about them - but is it possible to put channels on it?
You can cast it from the web gui to the Google Home. I did this with a football game. The only native ways I know of to watch video on the home hub would be YouTube or YouTube TV, but casting from the web ui is supported.
I'm not sure about casting live tv and not home today so I can't try it. Casting recorded shows does work.