However, that leaves open the question of why it did prosper. This seems a good explanation and suggests the success was down to the hard work of Paul of Tarsus who changed it to make it more appealing. It also says that it proved popular psychologically because it coupled
a coherent and attractive picture of how the world worked with a commonsensical moral code.The Christian idea of the afterlife was much more attractive than that of other religions and, for that reason, appealed to those who had a crappy time in this life. Their reward, so palpably absent from their day to day existence, would become apparent once they were dead. Plus it also gave people a place in the Universe and the illusion of control over their lives.
The Christian God was also a nicer guy than those old pagan deities. The older faiths were all about anger and punishment, plus they were very parochial whereas God was about forgiveness and was universal. And, in Christ, there was an explicit connection to humanity.
Christians were also heavily persecuted during the early days. The Roman games were all about punishing Christians as well as lots of other enemies of Rome. Some Emperors tried to stamp it out by burning books, destroying churches and killing worshippers.
There were alternatives to that early Christianity too. Notably Mithra and the Sol Invictus cult of Rome. Plus there were a lot of mystery cults that disappeared without a trace. Around Europe there were a lot of Pagan religions that were steam-rollered by Rome and then Christianity came along to fill the void in their wake. More so when Christianity became the dominant religion of the Empire.