How we know whether the origin of metamorphic schists and aluminous gneisses is marine sediments or immature continental sediments. What geochemical or petrological evidence is more appropriate?
1. Have a look at the metamorphic lithologies associated with your rock under study; are there meta-carbonates, metabiolites...etc. Sometimes you can get an impression of the hidden paleoenvironment. Even by the presence of strange minerals like scapolite (ref. palaeo-sabkha..) you can get a hint.
2. Use ACF, AFM and AFK diagrams where the protoliths are shown by reference fields
3. Try and find ultrastable minerals like rutile, tourmaline and zircon. A very subtle investigation of them microchemically and morphological may in some cases shed some light on the parent material pointing to nearshore marine. You can get an idea of the state of maturity.
4. Try an determine the boron content (marine higher than continental) and consider the Al content; extreme or abnormally high amounts may direct your view to meta-bauxites or meta-(duricrusts).
Take a multiple approach to this complex topic encompassing geological (1.), chemical (2) and mineralogical (3) methods.
There is no single simple technique. Professor Dill is on the right path. You need to look at everything, lithology especially - as above - are there any rocks that were carbonates, are there metamorphosed conglomerates, do the meta-sandstones retain any sedimentary structures such as cross-bedding, graded bedding, wave oscillation ripples? I suspect that marine successions will be more likely to be preserved than continental successions, but that cannot be assumed. Are there any fossils remaining in the metamorphics?
See B. P. J. Stevens & G. M. Bradley (2018) Sedimentology in metamorphic rocks,
the Willyama Supergroup, Broken Hill, Australia, Australian Journal of Earth Sciences, 65:1, 25-59,
There is no specific method to determine the source of the protolith but I suggest you use the PIA (Plagioclase Indexe of Alteration, loyd & Leveridge, 1987) and CIA (Chemical Indexe of Alteration, Nesbitt & Young, 1982) or the PIA vs. CIA diagram. The mineralogical maturity can also be portrayed by Log (Na2O/K2O) vs. Log (SIO2/Al2O3).
You can also use provenance characterization diagram (Floyd & Leveridge, 1987) and discrimination diagram for sedimentary provenance based on major elements (Roser & Korsch, 1988).