As I understand it, one of the key contributors to Christianities spread was its heavy emphasis on outreach and proselytizing, while most of its contemporary faiths were either only interested in spreading themselves to a certain region if they were that concerned about converting new believers at all. Where there any other precursors or contemporaries to early Christianity which also had a strong emphasis on sending out missionaries and spreading the faith?
Buddhism was already established when Christianity arose, and Ashoka sent out missionaries in the 3rd century BC. These previous answers go into more detail. /u/JimeDorje's comment is mostly outside your period but the basic patttern is relevant.