Select "The Dredgers" from the Mystery menu option when beginning your game. This option is defaulted not have a mystery occur in your game. For the greater part of your first 100 Sols, nothing will happen with the mystery. The first event is a warning of more meteor showers and a notification will pop up called "Mystery Log" which you can't remove until the Mystery is completed.
Currently unsure when exactly the game decides that you are far enough to begin the Mystery, but it was around Sol 80ish for me. I was playing Russia and going for their Sol 100 Achievement (Gagarin's Legacy).
They are mostly a nuisance that come and steal resources from you and you have to just deal with it in the beginning. You are initially only allowed to scan them.
This mystery has a couple breakthrough techs that are super high science (20,000) to research but are shortened by interacting with the dredgers.
Eventually you can use drones to dismantle the dredgers to stop them taking resources as well as speeding up a breakthrough tech, but eventually you have a final point where very large dredgers will land and you'll have to destroy them too.
Worth noting that I don't know whether that ultimatum always happens or only if you dismantle a lot of dredgers. The game's final notes on the entire event suggest that there may have been another option, but that would mean giving up some if not all of many of the resource deposits all around the map. The game has mechanics to keep resources plentiful, but it would require a much different approach from the beginning.
EDIT 1: According to Augustinoi, 100 Colonists is the trigger.