Before I begin, I would like to say that I am a scientist. I have been an atheist for most of my life. I recently became a Christian but I do NOT believe in religion.
Religion is following a set of rules, which can be oppressing. Jesus didn't seem to believe in rules either, as he and his disciples often got into trouble with the religious authorities for breaking rules like eating with unwashed hands.
Science is the study of the physical world. The various disciplines, e.g. physics and biology, focus on different aspects and see the same events in different lights. For example, in the scenario of a cat dropping to the ground, a physicist and a biologist would each measure different properties from each other.
Jesus's claim that he is the Son of God is spiritual. It does not come under the scope of science. Of course I love science and believe that it is a fantastic tool that performs its task very well, but with fundamental questions like "Is there a reason why we exist?", "Is there more than just this physical world?", and "Why do we even bother asking questions like this or questions at all?" science has no definite answer.
I like some of the previous comments like a lot of religions being dead due to "druids" inventing gods to explain natural phenomena and the series of posts about the integrity of biblical sources as historical documents.
A point I want to make is a variation on the analogy of how difficult it would be to prove that "there is no gold in China". Imagine someone said that there is a silver pebble with green spots on it. Neither you nor me have ever seen one ( unless you have :P ), how do we decide whether such a thing exists or not? To be pragmatic, it is easier to believe that it does NOT exist until a situation arises where its concept is needed to explain something. This line of thinking is "If I have no knowledge of something, it might as well not exist". This is a very natural and practical way of thinking; imagine if you considered the possibility of everything you never encountered! But how sturdy is this rule at resolving the existence of something you have heard of but never personally witnessed? If you lived all your life in a tropical country and had no access to the media, if someone came along and told you about snow you would conclude that it doesn't exist. So imagine if you came across that green-spotted silver pebble; what then? Your previous conclusion would have been incorrect. "People don't rise from the dead!" What if one person did? Even if no one ever rose from the dead before or after this one person, that is no evidence to disprove that it happened the one person.
In conclusion, the best logical answer to determining the existence of something you have never witnessed is that it is EQUALLY RATIONAL to believe or not to believe in that thing. It is equally rational to believe that there is more than the physical world as it is to believe that the physical world is everything. It is equally rational to believe that there is a God as it is to believe that there is no God. I believe that there is more than just the physical. I believe God exists.