I know the Romans kept extensive records about all kinds of things, especially historically significant events. What about in palestine between 5bce-40ce?
The FAQ has a pretty good section about early Christianity and historicity of the Bible. There are a handful of answers that take different approaches to analyze the evidence we do and don't have to determine. Based on the wording of your question, I think you'd be particularly interested in this answer by /u/Celebreth:
For a more direct answer, there's this write-up by /u/talondearg: