Nope, no such button, I must be looking in the wrong spot.
when I click on the user name a few details com up.
then click on the downward arrow, a few other things come up, but can not see "start Conversation
You should have permission to start conversations now. 5 posts are required to start conversations, but the promotion into the user group which has permission to start conversations wasn't working properly. It should be fixed now.