First, the New Testament was not written "hundreds of years after Christ died." Because historians consider "living memory" to be approximately 180 years, even liberal biblical scholars concede that the New Testament was written within living memory of Christ and the apostles. Many scholars believe that the New Testament was completed by the end of the first century, which is within 70 years of the death of Christ. The books of the New Testament were not officially placed into the canon of Scripture by the Church for several hundred years, but they were certainly written well before that time.
The New Testament offers several lists of the names of Christ’s apostles, all of whom were men (Matt. 10:2–3; Luke 6:13–16; Acts 1:13, 26), and records that they were specifically chosen by Christ from among his disciples. It is the responsibility of those who claim that the New Testament is at best incorrect or at worst a falsified document to prove that assertion.