During the first few centuries of Christianity's existence, it was not even seen as its own identity, instead, it was seen generally as a sect of Judaism, as its practitioners shared much of the same beliefs and practices more Orthodox Jews believed in from the late Hellenic and early Roman period. In order to understand how Christianity was able to spread so much, it is important to understanding the historical context behind the arrival of Christianity in the first place, that is, the evolution of Judaism over the centuries leading up to the time of Jesus.

For much of its history, the Jews were centralized in modern day Israel, there were some key events, however, that allowed Christianity to spread across the Mediterranean in its early history. The third to first centuries BC saw Judaism change quite a bit under the influence of the Greeks. Among the nations Alexander the Great conquered included Judea (modern day Israel). Judea would continue to be ruled by the Greeks during the time of the Seleucid Empire, until the time of Antiochus IV, when the Maccabees revolt against the Seleucids, and the Jews reclaim Judea under the Hasmonean dynasty in the mid second century BC. The main source of the Maccabean Revolt are the two books of Maccabees (the Catholic and Orthodox churches consider Maccabees to be part of the Bible, Protestant churches usually do not), the first century Jewish historian Josephus also talks rather extensively of the Revolt in The Antiquities of the Jews, and in the first chapter of The Jewish War.

By the time of Jesus, Greek culture had already had a rather profound influence on Judaism. The most obvious influence was the translation of the Hebrew Bible (i.e. what Christians call the Old Testament) into Greek in the second century BC (i.e. the Septuagint), the New Testament was also originally written in Greek, whenever a New Testament author quotes the Old Testament, they quote from the Septuagint, rather than from the original Hebrew. Greek culture appears to also have influenced certain theological beliefs of Judaism during the late Second Temple period, especially with such concepts like Heaven and Hell. Much of the Hebrew Bible is noticeably silent on explicit mentions of a Hell-like afterlife, with reward and punishment in the afterlife appearing much later, such as in the Book of Daniel. It is believed that the modern depictions of Heaven and Hell which are described in Daniel and in the New Testament have been inspired by Greek mythology, the Greeks had a concept of a good afterlife (Elysium) and a bad one (Tartarus) by the fourth century BC as Plato describes such an afterlife in The Republic.

Though it is likely Jesus’ theological viewpoints were inspired by the Hellenized aspects of Judaism, it seems that Jesus only preached within Judea (which was at this point a Roman province), there are no mentions of Jesus preaching outside of Judea, or of him attempting to convert the gentiles; quite the opposite, in fact, as Jesus supposedly gave his apostles the order to not interact with the gentiles (Matthew 10:5). Despite Jesus’ prohibition to interact with the gentiles, the concept to convert non-Jews to Christianity arose very early on.

The earliest known instances of Christianity spreading outside of Judea come from the ministries of Paul, the New Testament depicts Jesus as preaching only amongst the Jews in Judea, whereas Paul wanted to introduce the teachings of Jesus to the gentiles throughout the Roman Empire. The earliest Christian texts we have are the letters of Paul to Christian churches across the Empire written in the mid-to-late first century AD. It is clear from the contents of the letter that during the time of Paul, there were small Christian sects dispersed throughout the Empire, especially in Greece and Italy, as his letters are addressed to churches in Rome, Ephesus, and Philippi, among other cities in the Mediterranean. Christianity’s growth into a world religion, however, was a slow transition that occurred over the span of many centuries, there was not a single event that changed things right away.

For the spread of Christianity in the Roman Empire up to the time of Constantine, u/midwesternphotograph has a wonderful explanation.