My feeling is that scientific method has the power to account for and interlink all phenomena in the universe, including its origin, using the laws of nature. But that still leaves the laws unexplained. Scientists normally accept the laws as “given”; explaining the laws of nature is above their pay grade. Cosmologists have attempted to account for the day-to-day laws you find in textbooks in terms of fundamental “superlaws”, but the superlaws themselves must still be accepted as brute facts. So maybe the ultimate laws of nature will always be off-limits to science. I hope not, but it’s hard to know what form a scientific explanation of laws would take. A final caution: the ultimate laws to which scientists refer may turn out not to be the eternal, immutable, universal, precise, pre-existing mathematical relationships that scientists assume. Maybe the laws and the universe came into existence together. Then we’d have to find another explanation for physical existence.
Is there anything science should not try to explain? Science is knowledge and knowledge is power – power to do good or evil. Sometimes ignorance is bliss. It is possible that a scientific discovery will be made that humans will later regret because it has awful consequences. The problem is, we probably would not know in advance and, once the discovery is made, it cannot be undiscovered.