How can you trust the New Testament if it's not scientifically proven?

This is an untenable objection because: For the scientific method to work the event in question must be observable, measurable, and repeatable. History is not measurable or repeatable, so the scientific method does not apply to historical events. It would be like trying to apply the Pythagorean theorem to a poem.
History uses the evidentiary method, not the scientific method. The evidentiary method is what is used in a courtroom to try a case of law. In this context the reliability of the New Testament rests on eye witness testimony. The New Testament stands as a collection of eye witness accounts. Just as a jury is employed to determine if the evidence is to be trusted in a court of law, each is called upon to decide the validity of Jesus’ claims based on the eye witness evidence recorded in the New Testament.