Is it true?
When were the Gospels and Paul's letters written?
Within living memory of Jesus, and one creed goes back to the first few years.
A common claim is that the stories about Jesus were written down centuries later. They were not. Mainstream scholars date the whole New Testament to the first century.
Paul's letters come first. Almost all scholars agree that Paul wrote at least seven of the letters under his name, and they date them to the 50s AD, about twenty years after the crucifixion.
In 1 Corinthians 15, Paul passes on a short summary of the faith that he says he had received from others. Most scholars think this creed is older than the letter itself, and many date it to within a few years of Jesus's death. Even the sceptical scholar Gerd Lüdemann placed its elements in the first two years after the crucifixion.
The Gospels came a little later. Mark is usually dated around AD 65-73, Matthew and Luke around AD 80-90, and John around AD 90-100. Exact dates are debated, but all of them fall within the lifetime of people who knew Jesus or knew His first followers.
Paul's letters: the 50s AD
1 Thessalonians is dated around AD 51 and 1 Corinthians around AD 53-57. There is strong consensus that seven letters are Paul's own: Romans, 1 and 2 Corinthians, Galatians, Philippians, 1 Thessalonians and Philemon.
Sources
An early creed in 1 Corinthians 15
The summary in 1 Corinthians 15:3-8 is widely accepted as older than Paul's letter, probably from the Jerusalem church, and formulated within a few years of the crucifixion.
Sources
The Gospels: about AD 65-100
Common scholarly ranges: Mark about AD 65-73, Matthew and Luke about AD 80-90, John about AD 90-100. Bart Ehrman puts Mark at AD 70-74.
Sources
My verses
For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that He was buried, that He was raised on the third day according to the Scriptures, and that He appeared to Cephas and then to the Twelve. After that, He appeared to more than five hundred brothers at once, most of whom are still living, though some have fallen asleep. Then He appeared to James, then to all the apostles. And last of all He appeared to me also, as to one of untimely birth.
Only after three years did I go up to Jerusalem to confer with Cephas, and I stayed with him fifteen days. But I saw none of the other apostles except James, the Lord’s brother.
Many have undertaken to compose an account of the things that have been fulfilled among us, just as they were handed down to us by the initial eyewitnesses and servants of the word. Therefore, having carefully investigated everything from the beginning, it seemed good also to me to write an orderly account for you, most excellent Theophilus, so that you may know the certainty of the things you have been taught.
This is the disciple who testifies to these things and who has written them down. And we know that his testimony is true.
For they themselves report what kind of welcome you gave us, and how you turned to God from idols to serve the living and true God and to await His Son from heaven, whom He raised from the dead—Jesus our deliverer from the coming wrath.
Further reading
Links open independent sources, not church websites.