There's a station in orbit of Pontus (gas giant) in the Galatia system, called Galatia Academy station. Select, "request a meeting with the provost" once you've gotten there.
After the conversation tree, you'll be given a new contact at the station, so open Comm Directory and talk to the contact with an exclamation point.
Proceed to do missions for that contact. After you've done enough mission for the contact (or maybe the right ones, not sure the exact trigger), the more story line heavy missions will start from there as well.
I'll note in my first run without tutorial, I also eventually got a highlighted bar mission randomly that directed me to that station as well, as I was ignoring the story line in favor of colony build up at the time.