John's gospel was written by the disciple himself. Paul was first-person contact with Jesus, Peter and James (the Lord's brother) as well.
Paul cites in Corinthians that there are numerous people who saw Jesus after his resurrection and were still alive, and he suggests to the Corinthians to talk to them about it.
If you want to get into a "written up long after" situation in regards to sacred books the Quran/Koran is an excellent example. But one cannot say that about the Bible and be intellectually honest about it.