Dionysius said:
in fairness, the oral stage lasted quite awhile.
in the sense that no major transcriptions of the new testament were made.
What is most likely is that after Jesus died and his followers recovered from the shock, they banded together. This core group would have been those who knew Jesus well and had spent time with him. Their personal experiences would have sustained their faith and been demonstrated to non believers some of whom would have been converted. It is likely that the first christians (apostles and other followers) would have told their personal stories of Jesus to others and spread interest in christianity that way: "I remember a day on the road to Nazereth when Jesus called me aside and told me..." or "there was the time when I got angry at Simon and Jesus looked at me and I knew I had been wrong and then he smiled and I knew forgiveness..." etc. As long as there were people who could relate first hand stories of Jesus there was no need for any written record. Written records are dry and lifeless compared to a story told by someone who was actually there. And there could easily have been several hundred followers all telling their versions of what Jesus did and meant when he spoke. Imagine how many different oral traditions there were? One family told these tales, a different family told other tales.
As the years passed and those who were eye witnesses to Jesus' life died, the christian communities had fewer and fewer story tellers. The next generation began to take over: "My mother told me of the day Jesus spoke by the Sea of Gallilee, She wept when she told me what he said. 'Blessed are the' ..."
So between 20 and 40 years after the death of Jesus literate followers would begin to collect the stories told by members of their church. These texts would have been the basis for the gospels. I'm sure many of the stories were misremembered, embellished or just plain wrong. They did the best they could in an illiterate world where written material was subject to easy destruction.
350 years after Jesus' death (the equivalent of 1650 to 2000 AD) when the church tried to agree on a cannon, they had to sort through hundreds of texts and figure out which they thought were most likely to be the most accurate and not step too far outside of the current church doctrine. They would have had to collect copies of texts used by churches all over the mediterranean world and go through them. Tough job.
Those first christians were incredible salespeople and convinced many people to convert. They did it through the one on one interaction with people. If you are a christian, most likely, you will say it was god speaking through them; if you are not a christian, you will find another reason for their ability to convert peope. But in any case convert people they did. True or not, the message they told one on one was very powerful.