(I'm only talking about the TV show here. The radio show was a different beast, an alternate reality. In that one, Chester's last name was Proudfoot. Doc was a drunk who fell from grace because he possibly performed back alley abortions. Marshal Dillon and Miss Kitty were definitely fucking, although it was uncertain if she was being paid for it. Never mind that. My thoughts regard the TV show, where Chester's last name was Goode, Doc only drinks every once in a while and probably doesn't know how to stir a fetus out of a woman and Matt Dillon and Kitty, while very good friends, were clearly not in a romantic/sexual relationship no matter how much people wished for it.)
There was never an origin story for GUNSMOKE. One day, America started tuning in to the adventures of Matt Dillon, US Marshal, and his friends in Dodge City around the 1870's. We know very little about the characters before they arrived in Dodge City. We know that Matt was an orphan who fell into criminal activity before he became a lawman. We know that Chester came from the Appalachians, like his replacement, Festus. We know that Miss Kitty was previously in Louisiana, probably New Orleans, before coming to Kansas. But we don't know anything beyond that. We don't even know how they met.
I had an odd moment on Friday as I was watching that night's episode. (I watch them on the 50th anniversary of the day they originally aired, so that night's episode had debuted on November 7, 1964.) There's just a way that the characters interact with each other that led me to think about how they came together in the first place.
I think Doc was the first to come to town, probably before the Civil War began. People trust him a lot, as if they've known him for a long time. He's got a solid reputation. I wouldn't be surprised to learn that he'd set out his shingle before the Longbranch opened its doors.
I think Chester came next, maybe in 1870, but he never really hung out with Doc. They knew each other, but I don't think they were friends. And then Miss Kitty bought the saloon (or at least the majority interest she had when we first met her; years later, she would become the sole proprietor) that she would turn into the Longbranch. I think Doc drank there and performed services for Kitty's girls, and they formed a friendship because of this. When you see the two of them interact on the show, even in the early years, it's like they've known each other forever, even before Matt Dillon came to town.
Which is why I think Matt showed up last. I don't think he'd been marshal for very long before we first met him in the series premiere. I think his path crossed with Chester's, and the two of them fell in together. As a marshal, he had to rely on Doc, the only doctor in town. Through Doc, he met Kitty. Through Matt, Chester became close friends with the others. And so the original quartet was formed.
We know how Quint came to town. We know how Festus came to town. And, while I'm getting ahead of myself (seeing as how it's 1964 in the GUNSMOKE lobe of my brain), we know how Thad and Newly came to town. But not even the books from the past 20 years, which are considered canon, have explained how the original group met each other. (Although one of them tried to explain what happened to Chester after Festus showed up. It's thought that he became a farmer, although anyone who knows Chester knows that he has an aversion to physical labor, not to mention the fact that the one time he tried that on the show, he was a resounding failure at it. In my opinion, he met a girl and started a family elsewhere. He always was a ladies man.)
The one man who would know for sure, John Meston, who created first the radio show and then the TV show, has been dead for almost as long as I've been alive, so we'll never know.