To improve on the analogy in the image to the left, let us compare science to our sense of touch. We can touch things that have color, but we cannot touch color itself. If color represents God, science represents our fingers. We don't expect to find scientific evidence of God because God is not a natural entity. Science is just one academic field that helps us gain a better understanding of our world.
But while science cannot test God, there are other things that testify to His existence. The best field, for lack of better term, is history. The Bible is flooded with historical narrative, testified to by actual eyewitnesses, as well as contemporaries.
Because of this, we can assess its reliability in the same way we assess other historical documents. Think of any historical fact you learned in school, then ask how you know it's true? By default, I tend to think of Henry VIII's many wives. Science didn't tell me he had 6, history did. We can't scientifically test this, because marriage is not a scientific concept. You could find a husband and wife buried together and still not know for a fact that they were married.
What's of particular note is that, as historical records go, the Bible is actually the strongest. A lot of what you accept as historical fact is actually based on very scant evidence, sometimes only on a single document. It's often even the case that these documents were not written by contemporaries, but by later historians.
Compare this with the Bible, which was written mostly by eyewitnesses and contemporaries. The four gospels alone are extremely reliable. Two of them (Matthew and John) were written by people who directly witnessed the events they described. Mark was written by Mark, a follower of the disciples, and tradition holds that Peter actually had a hand in it. We can also add that this rules out pseudepigrapha (falsely attributed writings), because if Mark had been a forgery, it would have been more likely to attribute it directly to Peter, rather than this relative nobody who merely followed him. Luke was a physician and a historian, who sought to investigate and summarise the events surrounding Jesus' life for a noble leader named Theophilus. All of the above means we have four independent, yet consistent, contemporary witness testimonies to Jesus' life, death, and resurrection. Internal evidence, such as undesigned coincidences (the correlation of seemingly trivial details that match up between accounts) further suggest reliability.
We see, then, that first of all, science is not the source of all truth, nor was it ever intended to be. Second, of all historical truth claims, we see that the Bible is actually the strongest, even if we completely ignore divine inspiration. This is but a tiny sample of evidence for Christianity.