I am not sure if you are talking about original documents or copies here...The articles I've read show that around 24,000 ancient copies of the New Testament existed within 300-500 years of the actual events. Around three of those, and some odd fragments, can be dated to be within 100 years or less.
On the other hand, the earliest copies of the Annals of Tacitus, a Roman historian, can be traced to 1100 AD or so. And they've got about 20 copies of it from 1100 AD on. The earliest histories of Caesar, so my sources tell me, total about 10, and the earliest one dates around 900 AD. Pliny's got about 7 manuscripts, the earliest of which dates to around 850 AD. Tacitus and Pliny were contemporaries to the evangelists (Matthew, Mark, Luke, and John), and Paul, Peter, and Jude, and Caesar was only 50 years BC.
These numbers can be found on all kinds of Christian sites, such as this one. I've yet to see any atheist sites challenge those numbers or dates - or at least none on a cursory Google websearch, which surprises me. (Usually there'd be at least one, if not several, atheist sites fighting some claim or another a Christian makes about history.)
For copies this is definitely wrong. I have read texts from that time myself during latin classes in school, including "De Bello Gallico" from Caesar himself.
If you're talking about original documents - I have no idea how old the oldest Roman documents are, but what we have are faithful transcriptions (the Romans had a very well-functioning buerocracy) in addition to contemporary coins, statues and other stuff.
I'm not going to discuss the trustworthyness of the gospels or the bible here, since it is in no way relevant to the story and would open a shitstorm in any case.