Wasn't the New Testament written hundreds of years after Christ?
None of the New Testament books have a date of publication written on them. It probably will not surprise anyone that those who attempt to figure out from linguistic and historical evidence the date a certain book of the New Testament was written come out with very different answers. The assumptions one brings to the evidence guides that interpretation. For instance D.A. Carson, Douglas J. Moo and Leon Morris in their book "An Introduction to the New Testament" would date Galatians as being written A.D. 48. They would date the Book of Revelation as having been written A.D. 68-69. These two book are sometimes, not always, considered the first book and the last book written in the New Testament. I have taken Bible classes at both theologically conservative and theologically liberal schools. The more liberal schools would count those dates I just gave as hogwash. I think the more liberal scholars would place the last documents to be written about A.D. 150.
The oldest know copy of New Testament material is Papyrus 46 (P46). Some would date it as between A.D. 175-225. That would mean the originals would be before that time.
Count that the life of Christ was A.D. 3 or 4 and his death often considered to be about A.D. 33 or so, and all New Testament books being written after that point, then you don't really have hundreds of years, if you count the dates of P46 as valid.
However those of the more liberal theological camp would place those documents much later than their conservative brothers and sister in the other camp.
I'm not sure the assumptions you bring to the text to help you decide how you would date it. I'm also not sure of the assumption behind your question. However, I'm sure that I would not be able to convert someone to Christianity based on my dating system nor could I convince someone that it is wrong based on someone else's dating system. In this case, as in many others in life, we prove what we postulate.
"An Introduction to the New Testament" by Carson, Moo, Morris.