If Jesus died in 33 AD [wikipedia.org], then why was it first written about around 50 AD [answers.com]? How accurate can a detailed account be when it's written 20 years after the events?
I don't think 20 years is that long to wait to write something down. Is it uncommon to wait 20 years before writing one's autobiography? We don't usually think people have forgotten all the details or are fabricating stories of their own life, even if they are telling things that happened 20 years ago.
If you look through 1 Thessalonians (the book the link you cited lists as being the first book in the New Testament), it mentions Christians in a fairly large area. There's already an established community of Christians. This book isn't establishing a new religion, it's encouraging people who are Christians already. Given how important the resurrection is to Christianity, I don't think the Christians of the time would have bought it had Paul suddenly said "Oh yeah, I forgot to tell you these last 20 years, not only did Jesus die for us, He came back to life too!"
Most of the early teaching of Christianity was oral. If you notice, Paul wrote many of his epistles while he was in prison. It may be that they early Christians were too busy travelling around preaching to take the time to write down a complete account. Maybe as they decided to settle down, they also decided to write a more permanent record of the things they had been teaching most of their lives.