The author of the Revit model should activate “Export base quantities” with the IFC export on the “Property Sets” tab. And preferable (with recent Revit 2023 or 2024 versions and an up-to-date exporter) also the “Export material property sets”.
That said, the exact quantities per material are not exported this way.
What you can derive from the exported IFC is e.g. the NetSideArea #307 of a wall, e.g. from the IfcElementQuantity (which is a set of quantities):
#301=IFCQUANTITYLENGTH('Height',$,$,2999.9999999871293);
#302=IFCQUANTITYLENGTH('Length',$,$,6830.0000000000027);
#303=IFCQUANTITYLENGTH('Width',$,$,369.99999999999994);
#304=IFCQUANTITYAREA('GrossFootprintArea',$,$,2.5270999999999884);
#305=IFCQUANTITYVOLUME('GrossVolume',$,$,7.5812999999674773);
#306=IFCQUANTITYAREA('GrossSideArea',$,$,20.489999999912101);
#307=IFCQUANTITYAREA('NetSideArea',$,$,20.489999999912101);
#308=IFCQUANTITYVOLUME('NetVolume',$,$,7.5812999999674835);
#309=IFCELEMENTQUANTITY('0qp_x20PzdpMcqFde$A9Dt',#18,'BaseQuantities',$,$,(#301,#302,#303,#304,#305,#306,#307,#308));
The thickness of material layers #270 (IfcMaterialLayerSet), e.g. 10cm for the last layer #269 referring to material #257:
#257=IFCMATERIAL('C3A_pleisterwerk_wandbekleding');
#265=IFCMATERIALLAYER(#228,90.,$);
#266=IFCMATERIALLAYER(#233,30.,$);
#267=IFCMATERIALLAYER(#241,100.,$);
#268=IFCMATERIALLAYER(#249,140.,$);
#269=IFCMATERIALLAYER(#257,10.,$);
#270=IFCMATERIALLAYERSET((#265,#266,#267,#268,#269),'Basic Wall:C3A_21_WA_LB_spm 90-30-100-140-10');
and the density of each material (e.g. for material #257)
#880=IFCPROPERTYSINGLEVALUE('Name',$,IFCLABEL('pleisterwerk - gips'),$);
#881=IFCPROPERTYSINGLEVALUE('Description',$,IFCLABEL('Plaster of Paris'),$);
#882=IFCPROPERTYSINGLEVALUE('Keywords',$,IFCLABEL('thermal:solid'),$);
#883=IFCPROPERTYSINGLEVALUE('Type',$,IFCLABEL('Solid'),$);
#884=IFCPROPERTYSINGLEVALUE('SubClass',$,IFCLABEL('Plaster'),$);
#885=IFCPROPERTYSINGLEVALUE('Source',$,IFCLABEL('Autodesk'),$);
#886=IFCPROPERTYSINGLEVALUE('Density',$,IFCMASSDENSITYMEASURE(1300.),$);
#887=IFCPROPERTYSINGLEVALUE('Emissivity',$,IFCREAL(0.90000000000000002),$);
#888=IFCPROPERTYSINGLEVALUE('Behavior',$,IFCLABEL('Isotropic'),$);
#889=IFCPROPERTYSINGLEVALUE('TransmitsLight',$,IFCBOOLEAN(.F.),$);
#890=IFCPROPERTYSINGLEVALUE('Permeability',$,IFCVAPORPERMEABILITYMEASURE(0.),$);
#891=IFCPROPERTYSINGLEVALUE('ElectricalResistivity',$,IFCREAL(2000000.0000000002),#64);
#892=IFCEXTENDEDMATERIALPROPERTIES(#257,(#769,#880,#881,#882,#883,#884,#885,#886,#887,#888,#889,#890,#891),$,'Thermal');
These numbers can then be used to make a reasonable guess on the available material quantity. Beware of the units in your model, though. I’m not aware of a direct way to export material quantities. I’ve tested with a Material Takeoff Schedule to be included with the IFC export, but this skipped over the individual material properties, alas.
If the user has modelled each material as a separate element, you can use the element quantities directly.