The first colonies on Mars were established in the early 2020’s with adverts on Earth promising a new “start”, other outposts would be established on the moons of Jupiter and Saturn as well as the continuing expansion of the early Lunar base and the establishing of other outposts on the moon and within the asteroid belt.
The first had been established beyond the Solar System (just before the first FDD was built and demonstrated) when a moon with breathable atmosphere was settled in 2083 in the system of Proxima Centauri.
The creation of the faster-than-light propulsion opened up various possibilities for colonisation and soon huge ships would be departing for new worlds all in the hope of finding a new home out amongst the stars. Corporations were also keen as there was money to be made in new metals and other as yet undiscovered resources.
Occasionally a suitable world would be found but there would be a problem with the atmosphere. Terraforming technologies that had proved so successful on Mars would soon be employed to transform worlds into habitable places where humans could live without breather suits (it’s what soon became called a “shake-and-bake” colony).
With overpopulation a huge problem on Earth, people would pay or do almost anything for a fresh start on another world. Roles that need to be filled are everything from farmers to engineers to scientists.