That is one important aspect, but there are several to my mind

- Life in the bronze age was very rough, and quality of life in cities was basically inhumane. Women were highly represented among earliest converts, as Christianity comparatively was rather progressive and demanded baseline respect for them. Also, pagan religions of the time, despite cultural significance, didn't promise much of a payoff for plebeians for all their toil. Conversion was easy after Paul pushed the case that they shouldn't have to convert to Judaism, with all that would entail.

- Especially in the early days, this was very much a pacifist religion, in addition to having an apocalyptic fixation. To Rome, "Render therefore unto Cesar the things which are Cesar's" is a handy sentiment for the populace to have. They fought and won several uprisings just from the Jews who wanted their independence (and expected their forthcoming Savior would literally help deliver this), and the vast empire was beginning it's slow decline. Killing Christians and making martyrs out of them didn't make much sense in the long-run.

- There is a magic sauce in universalizing, it extends the shared culture within territories and makes it easier to convince people to wage war for you. Prior, the motivators were mainly tribal/blood connections, and money.

The Jews for their part were content with what they had, Christianity didn't provide much value-added, especially for the "zealots" who were ready to die for freedom. The "Love-thy-neighbor" sentiment is sort of similar to parts of Leviticus, but the cranked up pacifism and relaxed outlook over some rules was a departure. I think the "afterlife" bit was a lot more persuasive for gentiles. Then of course the rituals and conception in the collective consciousness evolved over time, from influences like Augustine and others.

By the time there was a true Christendom, powers that be dropped the (absolute) significance of pacifism, as that was no longer as useful as it was.