The New Testament was written hundreds of years after Jesus, so it can't be historically credible.

Your instinct about memory is sound, and if the gap really were centuries the Gospels would be worthless as testimony. The problem is that the gap is not centuries. It is roughly one generation.

1. The premise is off by two hundred years. Every book in the New Testament was written in the first century. Paul's letters run from roughly AD 48 to the mid-60s, and the Gospels from about AD 60 to 95, with skeptical scholars typically dating Mark around AD 70. No mainstream scholar, Christian or not, places them centuries later.

2. Paul writes within a generation. First Corinthians is usually dated to about AD 55, roughly twenty-five years after the crucifixion, and Galatians may be earlier still. These are letters written to living congregations while the events were still within living memory. That is not a folkloric gap; it is a newspaper cycle by ancient standards.

3. He passes on a creed older than his letters. In 1 Corinthians 15:3-4 Paul writes, "I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures, that he was buried, that he was raised on the third day in accordance with the Scriptures." The technical language of receiving and handing on marks tradition, and most scholars date that formula to within a very few years of the crucifixion.

4. He invites the audience to check him. Paul says the risen Christ appeared to more than five hundred brothers at once, "most of whom are still alive" (1 Corinthians 15:6). You do not stake a public claim on five hundred living witnesses in a city where they can be interviewed unless you believe they will corroborate it.

5. The genre is biography, not legend. Luke opens with the conventions of Greek historical writing, claiming to have "followed all things closely for some time past" and to write "an orderly account" (Luke 1:1-4). Second Peter explicitly denies cleverly devised myths and appeals to eyewitnesses (2 Peter 1:16). These authors are presenting themselves as reporting, and they name the sources.

6. The embarrassing material argues against invention. The Gospels record Peter's denial, the disciples' cowardice, family skepticism about Jesus, and women as the first witnesses of the resurrection in a culture that discounted women's testimony. Invented hero stories do not work that way. Legends embellish; these narratives keep the awkward parts.

7. Turn the standard on Alexander. The earliest surviving biographies of Alexander the Great were written centuries after his death, and no historian doubts the outline of his life. If a thirty-to-sixty year gap disqualifies a source, the critic has just discarded nearly all of ancient history, including the sources he uses to doubt the Gospels.

8. The manuscripts narrow it further. The John Rylands fragment, P52, contains part of John's Gospel and is usually dated around AD 125, within a generation or two of composition. Large codices follow in the third and fourth centuries. For an ancient text, that proximity is extraordinary rather than embarrassing.

9. Hostile sources agree on the core. Tacitus reports that Christ was executed under Pilate, Josephus mentions James as the brother of Jesus called Christ, and Pliny describes Christians singing to Christ as a god. None of them was a Christian. They do not prove the resurrection, but they remove the option that Jesus was invented.

10. What is honestly disputed. Scholars argue about precise dates, about whether Matthew and Luke used Mark, and about how much John reflects later reflection. None of that is the same as "hundreds of years." The disagreement is about decades and sources, not about whether the events were remembered.

The objection would be devastating if its premise were true, which is why the premise is worth checking before the conclusion is drawn. By the standards applied to any other ancient figure, the New Testament stands unusually close to the events it reports.

Sources: Richard Bauckham; Jesus and the Eyewitnesses; Craig Keener; Daniel B. Wallace.

Related challenges:
• How can you take the gospels as inspired when they don't even make that claim for themselves?
• Miracle stories were crafted AFTER Jesus died, and then included just to make Jesus look like a Jewish wonder working messianic figure. It’s called messianic fiction.
• There’s no evidence outside of the Bible that indicates the miracle stories about Jesus are authentic!