Science limits itself to the observable and repeatable. It can tell me nothing about that which is not observable and repeatable.

In other words, the unfalsifiable.

To say we can know nothing that we can't repeat and observe ourselves is to say that a courtroom can never use eyewitness testimony to get to the truth of what happened beyond reasonable doubt.

I don't see how any reasonable person can consider the writings in the New Testament to be a reliable enough source to be used as evidence in a trial, much less as supporting evidence for extraordinary divine claims. There isn't any hard evidence I know of to show that the people who actually claim to have seen these events themselves are the ones who wrote it down (and that their writings were preserved unchanged). More likely this "testimony" was gossip passed down verbally before eventually being written down (and then translated again and again), and any preschooler can tell you how a game of telephone can mangle the original message. And that is generously assuming that the original message was a genuine and authentic reporting by a sane observer and also that those writing it down didn't take creative liberties with their writing or outright decide to fabricate lies (which makes sense when you consider the great political power that be gained through religion).

Extraordinary claims require extraordinary evidence. To believe in the Jesus of the Bible is to believe it is possible for a being that appears to be a man to die, rise from the dead, and then literally ascend to heaven, or to walk on water, or to turn water into wine (and if you don't believe in any of the divine claims about Jesus, then what basis do you have to take any of the metaphysical claims supposedly said by him any more seriously than any political dissident out on the street today). These are extraordinary claims that appear to violate our known laws of physics. The evidence for such claims has to be incredibly compelling for any reasonable person to bother taking it seriously. I wouldn't accept video evidence of such events as something that makes it worth looking into (since it could be easily doctored with modern technology) much less the written down gossip of people.