> presumably starting with a mere few dozen disciples--managed to proliferate so rapidly across different languages and cultures (from Rome to Egypt to Iran, etc.) despite facing competition and even persecution from other, previously established religions (such as those in India and the Roman Empire)

All those assumptions are questionable. There’s very little data on how Christianity got started and what happened for the first few centuries. Maybe it started with a few hundred followers and grew at a fairly “normal” rate, just a little faster than others.

In many places, Christians weren’t much persecuted. Ancient people were generally live-and-live about religion. Certain individual emperors would get concerned and try to persecute them, but their policies didn’t necessarily take much effect on the ground. Persecution often backfires and creates inspiring martyrs, then and now.

It does appear that fairly early on, the church was unusually literate and organized, which may have helped them grow faster than others. Maybe it was a coincidence from having a relatively urban, Jewish base. Also, the “established” religions weren’t really autonomous organizations, they were outgrowths of societies and ways of life. So, if you moved from rural Iran to Antioch, or were captured and enslaved, you might lose any connection to your original religion and be ready to pick up something new.