If terraforming Mars was a thing, it would realistically have to be a massive undertaking spanning dozens, if not hundreds, of Sols and a number of technological adjustments to even survive.
For starters, you need to find some method of creating a magnetic field for the planet. This can be done as described above or, if you're feeling truly eccentric or up for a challenge, and therefore a true Paradox fan, potentially digging down into the core and heating up the outer core enough to melt, then somehow giving it a spin, creating a natural magnetic field similar to Earth's. The process would be immense and possibly require shielding the entire colony and everything that'd be within the new magnetic field from what could possibly be a planet-sized EMP (if you believe massive shifts in magnetic fields can be considered an EMP, but even if you don't, remember that if you take a magnet near a monitor everything goes weird... equipment on Mars isn't meant to be used on Earth, so it's possible the sudden existence of a magnetic field on Mars could have serious consequences)
Secondly, you need to increase the density of the atmosphere through some method, most likely through use of something like the subsurface heater in mine form near the poles to rapidly melt large amounts of ice or some other machinery to tap into materials that can be easily converted into gasses, increasing atmospheric pressure enough to prevent water from evaporating. As you do this, you run into a serious power and transportation problem: all wind turbines, shuttle engines, and solar panels are all designed for use in the less-dense Martian atmosphere. Turbine designs would have to be modified over time to prevent them from being torn apart as the atmosphere becomes more dense, eventually being replaced with something similar to windmills on Earth. Solar panels would have to be designed for even greater efficiency as the atmosphere reduces the amount of light they receive. Shuttles, designed to rely on thrust in a relatively thin atmosphere rather than lift, will find themselves having a hard time moving as they suffer through increased drag and potentially require major redesigns. After that, you have to realize that dust storms are still a problem, but they're now powered by a denser atmosphere as well... This is necessary, however, because even when you factor out the high carbon dioxide content and low oxygen content on Mars, the atmosphere is too thin to be truly breathable. As the atmosphere becomes thicker, meteor strikes would become less common, perhaps replaced with shooting stars that boost the morale of colonists as they realize they're truly making Mars into something amazing.
Third, you have to start worrying about water. You can't make Mars green without surface water. This could be solved by either dropping comets into the Martian atmosphere or releasing water from deep underground deposits. The Core Water breakthrough could be used to help with the process, but doing so would mean you'd have to sacrifice large deposits of water, meaning that until it's on the surface in acceptable amounts, you have to accept your colony might not have any for a while... but it also results in the biggest concerns for the entire terraforming project for many colony sites. If you landed in a deep chasm, you could find your colony quickly flooded as that crater, canyon, or whatever becomes a lake or ocean. As the Sols pass, your colony would have to start building lifts from the domes to the expected surface of the future ocean or lake, construct platforms for surface buildings and rocket landings, design underwater drones and other technology, and adapt to an underwater lifestyle. In other areas, you might have parts of the map flood while others remain dry. As you do this, dust devils and dust storms would probably become less common, replaced by rain showers, thunderstorms and, possibly, tornadoes.
Once this is done, you can start worrying about making the atmosphere breathable. Depending on who you ask, this can be done through specialized bacteria, powerful machinery (perhaps a "super MOXIE"), or simply by cultivating larges amounts of open-air flora to slowly replace the carbon dioxide with oxygen. Once the oxygen content reaches a certain point, you can safely say that unsheltered life on Mars is now possible. Unless you happened to be in an area that's now underwater, there would be no reason to build domes anymore except to protect your colonists from the elements, no need for life-support suits. You wouldn't need MOXIEs or Moisture Vaporators. Throughout the process, your colony could witness the first rainfall on mars, watch the red soil turn brown, and eventually green with plant life. Animal life could be engineered in a lab or imported from Earth, creating a thriving ecosystem with a healthy food web...
If this was done, it would probably be the single most epic thing you could do in a game like this, every event and milestone being an achievement in its own right, every stage you finish with your colony intact being a reason to proudly say "I'm making this happen. We're making this happen." The first colonists went to Mars with the optimistic hope of simply surviving, but their descendants would be taming it, conquering it, making it into a new home for humanity so much like the blue and green marble their ancestors fondly looked at in the sky every chance they got.
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