One doesn't need to personally run experiments to reproduce science in order for the reproducibility of science to be effective at explaining the world. The fact that one can reproduce and observe is itself evidence. The great thing about the natural world is that we aren't required have to have faith in it, it exists as it is and if we want, we can pick it up and examine it. People don't have "faith" in science because science doesn't require it.

Unlike the natural world, the supernatural cannot be observed nor reproduced so it necessarily requires faith in order to function.

In more concrete terms: I don't know how my microwave oven works. I've never built one and don't have a degree in microwave oven technology. But I still don't need to have faith that it works--I can observe it working and if I wanted to, I could take it apart and observe its subcomponents working. I don't do this, but just the fact that I could means that I don't have to blindly believe in it or conjure up explanations about how it works.