Umm, akshually. The Martian atmosphere is already 95℅ CO2. Its cold because the atmosphere is so thin. Its thin because Mars does not have a strong magnetic field like Earth does, so solar winds can strip away bits of the atmosphere. Also, Mars only has about 0.38 times the gravity of Earth, making it easier for gases to escape.
Akshually akshually atmospheric escape is a very slow process and would take even a large atmosphere thousands or maybe even millions of years to disappear. You could add the atmosphere first and have plenty of time to figure out how to keep it second.
The atmosphere would still be a CO2 toxic hellscape, so we could only send billionaires there for a long time.
What if the second solution is some technology - godlike to people from our time - that could start spinning the core of Mars to create a magnetosphere? That might be more difficult with people already living there.
But that is an easily solved problem. Take the design of the James Webb, substitute the super cooled infrared camera and replace it with a superconducting magnet setup. Fly this setup to L1 of mars and start global warming.