Unfortunately, you cannot do that yet, if you are asking for automating the triggering of actions through a rest api for example and then the google home just starts answering, there is no rest api for that but this will be the proactive assistant functionality.
In Google IO 2017, they introduced a new concept coming to the Google assistant which is proactive functionality, some calls it notifications, which is allowing the google assistant to start the conversation with the user, to give him info about the traffic for example if he has to be in a meeting in time.
but they announced neither a time frame nor any information about it.
so if this is what you are looking for, you just have to wait.