The whole idea behind the scientific method is that reality is material in nature, is there any way that we could test this notion? All attempts by the scientific method to prove or substantiate the idea that there is matter that exists outside of observation fail, as does the idea that matter at it's most fundamental level is composed of something that we can call material, (it's just layer after layer of sub atomic particles and as far as anyone really knows we may never arrive at a fundamental indivisible particle) in this context is it possible to test the notion of materialism, is materialism falsifiable using the scientific method?
The fundamental assumption on which science ultimately rests is not the idea that reality is material. It is the idea that perception can provide us with, and is the only source of, reliable data ultimately issued from the phenomenon we are interested in investigating.
The idea that the world is material should probably be best regarded as the naïve and unexamined assumption that we almost all invariably arrive at and well before we can think rationally. We just call matter the stuff we perceive around us. Materialism, then, is just this idea elevated to the status of philosophical dogma. Nothing specifically to do with science.
Materialism HAS been tested, and it has been falsified.
The way to falsify materialism, is to look for difficult test cases. IE, is everything reducible to matter?
There is effective consensus among philosophers that the "hard problem of consciousness" has not been solved -- consciousness still MIGHT be reducible to matter, but the several centuries of failure so far, are strongly suggestive that this will never happen.
The "special sciences" do not reduce to matter. Philosophy of science has abandoned reductionism, and the theory of the "unity of sciences". See SEP's entry on Scientific reductionism, particularly section 5. https://plato.stanford.edu/entries/scientific-reduction/
Examples of the sorts of things that don't reduce to matter: Loyalty, The British Constitution, norms, etc.
Plus there are multiple non-science fields that don't reduce to science, yet sure seem to exist: Mathematics, logic, all the different kinds of aesthetics, ethics.
Physics itself has been pretty brutal to materialism. Einstein's general relativity showed that matter can be created and destroyed, IE we could have a universe with no matter. So-- not everything could be matter. Plus coming out of Quantum Mechanics, there is dark energy, virtual particles, and a probabilistic field -- which are not obviously "energy" either. The mark of matter is to have location and time, and basically nothing at the QM level has location nailed down, and are fuzzy on time too. And none of our particles even started out with any MASS -- they only got mass after the Higgs' Boson precipitated out from the background wash of previously indistinguishable massless particles! Cosmology has further undercut materialism -- all our matter and energy seem to have been created out of nothing by the process of Inflation, which may have leaked over from another universe -- violating causal closure for ours.
The issues in physics have led most materialists to abandon materialism as refuted, and instead adopt "physicalism". The problems for physicalist reduction have led most physicalists to adopt non-reductive physicalism, in which other non-physical things can emerge from physics. This non-reductive physicalism allows room for non-material, and non-physical things like qualia, memes, norms, mathematics, and beauty to exist.
Daniel Stoljar, in his book Physicalism, notes that virtually no physicalists today assert that nothing non-physical exists: https://www.amazon.com/Physicalism-Problems-Philosophy-Daniel-Stoljar/dp/0415452635 He then goes further, and shows, thru Hempels' Dilemma, that even this loose approach to physicalism cannot be defended -- that every effort to define physicalism as an ontology that can exclude things like ghosts and math from physics -- fails, in one way or another. Ether the definition is false, or it can't exclude the things physicalists want to exclude. Stoljar instead adopts an undefined "naturalism".
What Stoljar encountered, is that science is a methodology, it is not an ontology. Many materialists and physicalists have falsely presumed that "naturalism" precludes anything non-material, or non physical, but this is simply untrue. naturalism is just a methodology, called "methodological naturalism", and it allows for one to postulate multiple possible ontologies for our world that can match the observations we have.
The highly voted answers to this question articulate that clearly. Is naturalism falsifiable?
Note, naturalism, the thesis that everything in the world is evaluable by the methods of naturalism, IS falsifiable. We could discover subjects which are immune to the methods of empiricism, and reasoning. Gods, spirits, consciousness, aesthetics, and morality, are the main areas where non-naturalism is asserted. But we can do empiricism and reasoning about all of those, so it is actually reasonable to conclude that none of the candidates offered up to date for non-naturalism are actually non-natural.