Can the laws of nature change?

Answer

“The laws of nature” you say. There are a lot of them and you have to distinguish them.

The laws governing how elementary particles interact are the most fundamental.
As far as we can tell, by observing the spectra of very distant stars whose light was emitted millions of years ago, the laws governing the behavior of light and electrons have not changed appreciably. And because those interactions are described by theories where the other fundamental interactions (nuclear physics) also occur, there is good reason to accept those other interactions as immutable.

In addition, you have the laws that indicate how pieces of ordinary matter behave, which consist of about 10²⁶ atoms exist. These are complicated systems that can change in many ways, which can manifest themselves in laws that seem to change. A simple example is the law of fall: in our regions the acceleration when falling is 9.81 m/s2, but slightly less at the equator and ten times less on the moon.
But the general gravitational constant remains the same everywhere.

Not only do writers of children’s books fantasize, physicists sometimes do this too, and there have been theories that assumed that the strength of the fundamental interaction with (cosmic) time also changed. But, as mentioned, there is no compelling reason to believe it.