How did Christianity spread so fast?

Pliny the Younger (Roman governor) c. 61–c. 113 ADLetter 10.96, to the emperor Trajan 10.96.9–10

Many of every age, every rank, and both sexes are and will be brought into danger. The contagion of this superstition has spread not only through the cities but through villages and farms too. ... It is certain that temples almost deserted have begun to be frequented again.

A hostile witness from Bithynia, eighty years after the crucifixion.

Letter to Diognetus c. 150 ADLetter to Diognetus 5.1–5

Christians are not distinguished from other people by country, language or customs. They do not live in cities of their own, speak a strange dialect, or follow an odd way of life. ... They live in Greek and barbarian cities, as each one's lot was cast, and follow local customs in dress, food and the rest of life, yet they show a wonderful and admittedly strange way of life. They live in their own countries, but as foreigners.

The new faith spread through ordinary lives in every city.

Tertullian c. 155–c. 220 ADApology 37.4

We are of yesterday, and we have filled everything you have: cities, islands, forts, towns, market places, the very camps, tribes, town councils, the palace, the senate, the forum. We have left you only the temples.

Rhetoric, but meant to be believed by Roman readers.

Tertullian c. 155–c. 220 ADApology 39.6–7

It is spent ... to feed and bury the poor, for boys and girls without means or parents, for the old confined at home, for the shipwrecked, and for any in the mines, on the islands or in prison for the cause of God. ... "See," they say, "how they love one another."

Pagan observers noticed Christian care for outsiders too. Emperor Julian complained that the "Galileans" fed pagan poor as well as their own.

Origen of Alexandria c. 185–c. 254 ADAgainst Celsus 3.9

It is clear from this: Christians, so far as it lies with them, do not fail to sow the word everywhere in the inhabited world. Some, at least, have made it their work to go round not only cities but also villages and country estates, in order to make others too devout toward God.

Origen is answering Celsus, who had claimed Christians would not want everyone to become Christian. He adds that these traveling teachers sometimes refuse even food, and take only what they strictly need.

Eusebius of Caesarea c. 260–c. 339 ADChurch History 3.37

These distinguished disciples built on the foundations of the churches that the apostles had laid in every place, increasing the preaching and sowing the saving seeds of the kingdom of heaven in breadth across the whole inhabited world. ... distributing their possessions to the needy; then, setting out on journeys abroad, they did the work of evangelists, eager to preach Christ to those who had never yet heard the word of faith, and to hand over the writing of the divine Gospels.

Eusebius describes the generation after the apostles. The evangelists first gave their own property away, then traveled; he goes on to credit the power of the Spirit still working wonders through them, with crowds converted at a first hearing.

Julian the Apostate c. 386–c. 455 ADLetter 22, to Arsacius 22

Why do we not notice that their benevolence to strangers, their care for the graves of the dead and the pretended holiness of their lives have most increased atheism? ... The impious Galileans feed, besides their own, ours as well.

Julian is the pagan emperor trying to build a pagan rival to Christian charity. In this official letter to his high priest of Galatia he concedes why the Galileans were winning converts, and his word for Christianity in the letter is atheism.