Matter as conceived by classical physics doesn’t exist. So in that sense, materialism is trivially false. Nonetheless, most scientists believe that reality can be exhaustively described by the equations of mathematical physics. Hence, physicalism. The equations describe a universe that exists independently of, and long predates, human minds. Perhaps contrast traditional forms of idealism, mind-body dualism, or the idea that “consciousness collapses the wavefunction” (cf. Von Neumann–Wigner interpretation - Wikipedia).
Two forms of physicalism may be distinguished. “Materialist” physicalists believe that the stuff of the world is non-experiential. Quantum field theory (QFT) describes fields of insentience. “Non-materialist” physicalists, e.g. Galen Strawson, believe that the stuff of the world is experiential. Quantum field theory describes fields of sentience. If so, then the entire mathematical machinery of modern physics should be transposed to an idealist ontology.
The biggest challenge to “materialist” physicalism is the Hard Problem of consciousness. The biggest challenges to non-materialist physicalism are often reckoned the palette problem and the phenomenal binding / combination problem.
Two related distinctions are worth noting.
1. Perceptual direct realists believe that during waking life, we are directly acquainted with the mind-independent physical world. Inferential realists about perception believe that each of us is running a skull-bound world-simulation. Belief that one’s macroscopic world-simulation is mind-dependent should be distinguished from non-materialist physicalism. In my view, we have strong grounds for believing in a world-simulation model of perception; non-materialist physicalism is an interesting conjecture.
2. Traditional materialism and (“materialist” and non-materialist) physicalism are often associated with reductionism. Molecular biology reduces to quantum chemistry reduces to quantum field theory. Everything that happens supervenes on the underlying physics. However, if quantum physics is complete (i.e. no “hidden variables”), then reductionism is false. Wavefunction monism is true. Reality may be described by the universal Schrödinger equation or its relativistic generalisation. Most – but not all – wavefunction monists are also “materialist” physicalists. Even if non-materialist physicalism is true, wavefunction monism is not the recipe for a cosmic mega-mind. (cf. Is the universe conscious?) Decoherence threatens the integrity of humble human minds, let alone a deity.