Not even sure if this is possible but

Is it possible to trigger “hey google” or “ok google” from HA, what I would like is to be able to trigger a certain speaker or display and put it into a state of listening, like I have just said either trigger words.

I don’t think you can do this. I’ve been able to work around it using one smart speaker to activate another. For instance sending a TTS to my HomePods with something like “Alex, what’s the weather” but it seems like that is being restricted by speaker makers now, they often now block the request and I think it’s because they recognize that it’s Siri asking Alexa to do something, I have better success when I don’t use the default Siri voice.

You can do this with Alexa.
Using the Actionable notifications for Alexa you just relace any text you would use with dots …

Yesterday I was able to set up a Google Routine (to make an announcement on a GH speaker) by creating a HA Automation, with a Calendar event as Trigger and a helper input_boolean as Action from OFF to ON. I wonder whether this should let you do what you want.
On the other hand I am very interested to replicate to Alexa. So far I have not been able to use that helper input_boolean as a trigger in a Alexa Routine.

All good ideas thank you, maybe if I explain what I am trying to achieve.

When one of the family comes back in the house, the system knows who it is, and gives one of several random responses to them being home, for example, Father in law comes in, it says hi and if it’s after 4pm it will lower the blinds in his room and set up the lighting.

But he doesn’t always want that so, after the greeting I could get the system to ask him, Do you want the Blinds down, or Do want the light on in the office.

This is the point I need the google speaker or display to enter “listening mode” the equivalent of “OK Google” he can then reply “lights on in office” and voila, with the Google set to continuous conversation we have unlimited interactions.

I already have it giving different responses to different situations, like if my wife has been to the big shop, it will let me know when she is near to home, so I can help unload, etc etc.

Just need to trigger Google somehow.

Thanks for all your suggestions so far.