Many factors that facilitated the growth of Christianity within the Roman Empire in the 3rd century.
First, it was a relatively peaceful period, with good roads and relkatively safe and efficient means of travel and communication, allowing for a geographical spread of the new religion.
Second, even though there was some intermittent persecution of Christians, in general, Roman polytheists aloowed considerable freedom of religion so long as it did not interfere with the state cults.
Next, the development of the codex allowed for relatively convenient and inexpensive production of copies of the Bible (albeit still handwritten).
Finally, this was a period of religious and philosophical syncretism, in which many new and hybrid religions took hold, and some, especially Manicheanism and Platonism often were compatible with Christian beliefs.