Left side of the screen is where you can see your progress on the three story objectives. You should have a button to click on, to start the story quest, once it is unlocked with stability.
Just to add a visual representation to what Kulras is saying. On the left-side you’ll see Quest Echoes – clicking on them will allow you to start that Quest Echo, one after another provided you have the required Timeline Stability.
Yeah, you’re not the first one to say that and likely won’t be the last. I would agree that it’s not the most obvious thing to do…until you do it, of course. Hopefully it’s something that gets addressed in the future.