The opening voice-over for the series when it originally aired said it was one solar system. And no, it’s not our own, and no, that doesn’t imply FTL travel.
The Firefly universe clearly has some form of constant-acceleration advanced propulsion technology. Given that, it makes complete sense that you can fly to another star system in a matter of years, and flit about inside a solar system in a matter of days or maybe a few weeks for the longest trip. The Firefly universe also has suspended animation, terraforming ability, and gravity control. Given those things, here’s how it could have happened:
You send 100 robotic scout ships out to the 100 nearest candidate star systems. Some arrive in a few years, others take decades. They report back what they have found, a process that also takes years or decades. Or perhaps you don’t even need the probes - advanced interferometry telescopes can directly image nearby star systems, evaluate atmospheres, even look for life. So you find a good candidate system - one with a few big gas giants, hundreds of moons, and maybe a dozen inner planets. Maybe a star system around a red giant, where the ‘habitable zone’ is larger than our entire solar system. Then you send robotic probes to that star system to terraform the main planets.
Once the main planets look good, you pack up a large ship with a couple of hundred people in suspended animation and thousands of frozen embryos. The trip takes maybe 10-20 years. Once they arrive, they set up a colony on the best, richest planet. Once the colony is established, Earth starts sending convoys of large cargo ships and more passenger ships, transporting Earth’s culture and essential artifacts and historical material. The ‘central planets’ become rich, and over time they start terraforming the moons on the outer worlds. A couple of hundred years go by, and the ‘core worlds’ are fully technological and populated with billions of people. The outer worlds and moons are backwards and poor. A strong government arises that decides its best to keep those outer worlds poor because they are full of rabble rousers, and restricts trade to them and otherwise keeps them oppressed. War breaks out, and the browncoats on the outer worlds lose.
There’s your Firefly universe. No FTL, no aliens, no magic required. Gravity control would be the most magical part of the whole scenario.
Chronos: I’d be interested to hear your opinion after you see the second and third DVD’s. That’s where the real meat and potatoes of Firefly are. The pilot was good, but the next two episodes were only mediocre for Firefly. Starting at episode 4, the series really takes off. I think your opinion is likely to get much stronger yet.