Do the laws of physics evolve?

For many (most? all?) physicists, it's something like an axiom (or an article of faith, if you prefer) that the true laws don't change over time. If we find out that one of our laws does change, we start looking for a deeper law that subsumes the original and that can be taken to be universal in time and space.

A good example is Coulomb's Law, or more generally the laws of electromagnetism. In a sense, you could say that Coulomb's Law changed form over time: in the early Universe, when the energy density was high enough that electroweak symmetry was unbroken, Coulomb's Law wasn't true in any meaningful or measurable sense. If you thought that Coulomb's Law today was a fundamental law of nature, then you'd say that that law changed form over time: it didn't use to be true, but now it is. But of course that's not the way we usually think of it. Instead, we say that Coulomb's Law was never a truly correct fundamental law of nature; it was always just a special case of a more general law, valid in certain circumstances.

A more interesting example, along the same lines: Lots of theories of the early Universe involve the idea that the Universe in the past was in a "false vacuum" state, but then our patch of the Universe decayed to the "true vacuum" (or maybe just another false vacuum!). If you were around then, you'd definitely perceive that as a complete change in the laws of physics: the particles that existed, and the ways those particles interacted, were completely different before and after the decay. But we tend not to think of that as a change in the laws of physics, just as a change in the circumstances within which we apply the laws.

The point is just that when you try to ask a question about whether the fundamental laws change over time, you have to be careful to distinguish between actual physics questions and merely semantic questions. Whether the Universe went through one of these false vacuum decays is (to me, anyway) a very interesting physics question. I care much less whether we describe such a decay as a change in the laws of physics.

If the laws of physics "evolved", then the law governing this evolution would be your new law of physics, provided it is positivistically meaningful (i.e. it isn't last-Thursdayism) and we have enough evidence to say it is probable.

Note regarding your claim about biology and geology -- the laws of biology and geology do not evolve, much like the laws of physics (including those of biology and geology) don't evolve. Biological and geological structures evolve, much like physical structures (including biological and geological ones) evolve. I don't know how you conflate the two.

There are some hypotheses which claim an evolving set of values for certain physical constants -- (they're probably wrong, but fun to think about)

Dirac's large numbers hypothesis

Some numerological coincidences like $\frac{r_H}{r_e} \approx 10^{42} \approx \frac {R_U}{r_e}$, $r_e = \frac {e^2}{4 \pi \epsilon_0 m_e c^2}$, $r_H = \frac {e^2}{4 \pi \epsilon_0 m_H c^2}$, $m_H c^2 = \frac {Gm_e^2}{r_e}$ are used to claim that "values of constants changing over time", as some of these constants (like $R_U$, the radius of the universe, and anything with a subscript $H$, a hypothetical particle with the radius of the universe) clearly vary. Dirac also hypothesised that these coincidences could be explained with a varying gravitational constant, $G = \left(\frac{c^3}{M_U}\right)t$ (which is odd, because you expect a symmetry between space and time).

Brans-Dicke theory

This modifies GR by replacing $1/G$ with a scalar field $\phi$ picked via the field equation $\frac{\partial ^ 2}{\partial a^2}\phi^a_a= \frac{8\pi}{3+2\omega}T$ for some coupling constant $\omega$.

It is not the laws of Physics that evolve, it is our understanding of them which does. Well, I cannot prove that there exist constant a priori laws that the Universe obeys, but I sure have elevated this practically to an axiomatic state within my worldview. But what we call 'constants' obviously need not be fundamental constants - the only reason they were called like that in the first place is that the quantities appeared to be constant when they were first discovered. Hubble's constant is an excellent example: he observed that the Universe seems to be expanding with a constant velocity in all directions - an amazing discovery for a time when we didn't even have the Big Bang model, mind you! I can imagine how it might have felt at the time that this is a constant in-grained in the fabric of our Universe. Better understanding, and more precise measurements, however, show that in fact the expansion of the universe is accelerating, hence the constant increases in time. But it's obviously not the laws of Physics that changed, it's our understanding of them.