I have read that no one knows what preceded the Big Bang, but is this true? The Big Bang process (with or without inflation) followed known rules which “existed” prior to time zero. For example, some of the obvious rules of the game included: mathematics, conservation laws (symmetry), thermodynamic laws (energy conserved, entropy increases), quantum mechanics (uncertainty principle, locality, and probability waves), special relativity ($c$ constant, $E = mc^2$), and general relativity (equivalence principle). Thus, we know a lot about the environment which set the stage for our universe. I have read the previous answer to this question but do not think it is adequate. What am I missing?
All the "rules" you listed, which describe the Big Bang process and subsequent universe, are concepts of how forces of nature interact. The forces of nature themselves - strong nuclear force, weak force, electromagnetism, and gravitation - may have emerged, along with time itself, from the Big Bang process. Without time, the rules would make no sense.
Phase transitions in the early universe (prior to the first 0.01 second) may help explain how the four fundamental forces of nature defined themselves by a process of symmetry breaking. Prior to that, the rules you list may not have existed, contrary to what your question assumes.
However, if by Big Bang you mean the hot phase that was followed by expansion and cooling, it may have been preceded by pure vacuum energy which inflated extremely rapidly, cooling in the process, and producing a condition in which the potential energy of the vacuum was converted into the kinetic energy of matter and radiation. This scenario was proposed by Alan Guth in response to two problems with the Big Bang, the flatness problem and the horizon problem.
This inflationary universe would have been caused if a state of vacuum energy density was in a "false vacuum" or temporary vacuum, and suddenly fell to a state of lower energy density. The change could have been triggered by a quantum fluctuation. The result of transition to lower energy density would have been equivalent to expansion. When the false vacuum decays, the energy in it is released to form a hot, uniform soup, and this is where the Big Bang begins.
But this begs the question of where the false vacuum came from. Were the rules you describe applicable to whatever it came from? This question may seem like peeling layers from an onion, and never coming to a core. In order to find the elusive core, James Hartle and Stephen Hawking proposed the idea that, in effect, there is no core. Their No-Boundary Proposal said that very near the beginning, time emerged from space, and that the universe is finite but has no boundary. It seems to me impossible to describe this adequately without the mathematics, but here is a link to Stephen Hawking's lecture on the beginning of time.
The problem with Hartle-Hawking is that it needs a closed universe to work, and observations don't seem to agree with a closed universe.
Sean Carroll, a theoretical physicist at Cal Tech, wrote that the Big Bang, or the state of vacuum energy density that may have preceded it, is a "plausible hypothesis". There is no certainty about what the Big Bang arose from. Inflation is the most accepted theory.
The comment by the late Stephen Hawking (cited by Jim Johnson on Sept.6, 2015) may sound plausible to many of us, but his frequent mathematical collaborator, Sir Roger Penrose (knighted several years ago for his many contributions to physics), would've eventually disagreed.
Although not a proponent of any "multiverse" in spacetime, Penrose's Conformal Cyclic Cosmology (developed in 2010) provided for past- and future-eternality through separation of the "aeons" of a true universe by "timeless" intervals, within each of which all matter would've previously evaporated into energy: During the periods between aeons, the lack of rest mass would've prevented the formation or construction of any form of natural or artificial clock. This facilitated acceptance of his "Weyl Curvature Hypothesis", which preserves angles but not lengths in dynamic applications of geometry, and consequently might, without possibility of observational contradiction, provide for the thermodynamic equilibrium of one aeon to become the "Big Bang" of the next: If the usual assumption that the BB was subsequently (and very rapidly) expanded throughout our observable region (and, hypothetically, extremely far beyond it) can be accepted for its simplification of baryogenesis and other advantages over the Steady State Theory which had preceded it, Penrose's enhancement of the Big Bang Theory is hard to resist.
Its own observational proof, described in a collaboration of Penrose with Meissener, An, and other noted physicists, lies in several spots of "significantly raised temperature" in the Cosmic Microwave Background radiation: These spots have been convincingly interpreted by that collaboration as representing Hawking Radiation of the aeon preceding our own. The final version of their paper was released shortly before the Nobel Committee's award, which was officially based on Penrose's work (much of it in collaboration with Hawking) on the nature of black holes. (Black holes are not at all hypothetical: The existence of more than 90, initiated within the gravitational collapse of large rotating stars, has been inferred from the elliptical orbits still followed by their former partners in binary pairs, and the formation of an especially large one by a somewhat different process--the collapse of a large amount of interstellar "dust", in Sagitarrius A--was recorded astronomically only a few years ago.)
Penrose was awarded a Nobel Prize in physics in 2020 for his work on black holes, shortly after revision of his collaboration's work.