My turn to throw some ideas to the mix.
I'm going to try to explain it in a quick & short way.
In some point of our near future, an huge Coronal mass ejection (Solar storm) strikes earth, wiping nearly all advanced electronics, and destroying the power grid around the world. A lot of knowledge is lost as was electronic stored in these days. In other worlds, humanity gets back to XIX in a single day. This catastrophe, creates a huge humanitarian and economic crisis that makes to fall a lot of governments around the all the world. Millions of people dies by hunger (think how many food are lost with refrigeration or a proper way to carry it to the big cities) and diseases. Small and medium factions have wars to control food sources, and the few remnants of advanced tech that keeps working. Some religion factions blames science and the advanced tech for this chaos, and tries to wipe out all science and modern tech from the face of the Earth.
In the next hundred years, the Earth human population falls to around 1.500.000.000. Humanity begin to recover some lost knowledge and some factions begin to rebuilt from the ashes. This recover is unequal, as some tech/knowledge was less affected by the storm that other (Rockets not need computer to fly, etc...). However, there is a lot of mistrust around computers as a lot of people keep blaming it as the one of the causes of the fall.
The most science friendly faction begin to dominate all other factions, thanks to using more advanced technology and at some point, the whole Earth is under his control. At this point, the humanity tech level is like the 70's but less advanced in some points, and more advanced in others. Trying to avoid another future fall of the civilization that could wipe out the humanity , an plan is scheduled to send convoys of ark ships with the most advanced technology to explore and colonize nearby star systems. This ships will take hundred of years to travel to another star system, using nuclear engines, and carry enough people and materials to initiate a independent self-sufficient colony. The human crew will be frozen, except for a few crew members that will be wakeup along the travel to ensure that the ship can reach their destiny.
When this ships reach his destiny, all the people will be wake up. Quickly seeing this new bold region of space ready to explore and exploit, many of then will try to explore and make a life in the space in one or other way (mining, commerce, piracy, etc). Other will begin to build the colony using the ark ship as an space city or materials to build the colony in the most hospitable planet.
The game will be setup a few years before an ark ship arrival to a star system, so there is not yet well established factions or government beyond the colony itself.
NOTE: If we add FTL to the mix, we could explain that when the Earth is united, and before creating the plan of space arks, they found a relic alien ship on Mars. From this alien ship, they could recover some principles of a FTL propulsion system, allowing to create the plan of the space arks. The space ark ships only need a few years to travel to another star system as is a slow FTL propulsion (few times light speed in limited time). Each colony keeps being independent as they are too far to being dependent from Earth.