Is it possible to notify all teammates if a conversation has started? Yes, it is. And it’s simple. You need to assign the incoming conversations to a team shared with all your teammates.
When a conversation is started normally will be assigned automatically to the first teammate that has created the app.
To change this behavior you need to create a team to assign your conversation by default. Once you have created your team go to your App Setting
On the left menu go to Smart Assignment Rules
Once you are here change the assigner to your new Team just created.
That’s it! Now all the conversations will be assigned to the team you’ve just chosen.