Science restricts itself to naturalistic conclusions and methods because those are the conclusions and methods that are successful. This result leaves us with a question to answer: Why are supernatural conclusions and methods unsuccessful in science? There are at least three commonly proposed answers, but only one of the answers is arguably correct.
One proposed answer is that imagined supernatural explanations automatically convert to natural explanations the moment they are determined to be true. In other words, everything that is true is ipso-facto natural. To demonstrate that this answer is wrong all we need to do is give an example of something that could be both true and supernatural. For example, if stars gave off light energy without consuming any energy then we would discover this fact. Having discovered that no physical, material, or mechanical process is involved in the production of star light we would be justified in concluding that star light is a supernatural phenomena.
Another proposed answer is that naturalism is intrinsic to science. Under this scenario, science presupposes naturalism and is incapable of obtaining knowledge via supernatural methods. To demonstrate that this answer is wrong all we need to do is give an example of obtaining knowledge via a supernatural method. For example, if the previously unknown answers to any question in mathematics were magically revealed to worshippers of Jupiter then we would be justified in concluding that Jupiter may be a supernatural God.
The one good answer is that science restricts itself to natural methods and conclusions because our universe is strictly naturalistic. People ask atheists for evidence that there are no gods. Here is the evidence: The monopoly of naturalistic methods and conclusions in science is substantial positive evidence that we live in a strictly naturalistic universe.