Context. Organic macromolecular matter is widespread in the Solar System and is expected to be a dominant carrier of volatile molecules in chondrites. Despite its prevalence in primitive Solar System bodies, its formation pathway is still unclear. Possible scenarios include formation in the interstellar medium, in the early solar nebula, or on planetesimals. Aims. We investigate the formation pathway of organic macromolecular matter via the energetic irradiation of simple ice analogs, mimicking the composition of an early Solar System ice. The organic macromolecular matter created in this way is suggested to resemble the insoluble organic matter found in primitive Solar System bodies. Methods. H₂O:CH₃OH:N₂ mixtures were co-deposited at 10 K onto a vacuum grade aluminum foil attached to a copper sample holder, forming an early Solar System ice analog. The ices were irradiated using 5 keV electrons, and after the irradiation, the aluminum foil was heated above the water desorption temperature. The remaining residues were irradiated again, forming organic macromolecular matter. The carbon structure of the residues were investigated using Raman spectrometry. The characteristic D and G band positions and full width at half maxima were compared to results from organic macromolecular matter in meteorites and interplanetary dust particles. Results. The G band position and full width at half maxima of the investigated residues show similarities to the results obtained by investigating the organic macromolecular matter in interplanetary dust particles. Furthermore, the G band properties indicate that the macromolecular matter formed via the irradiation of simple ice analogs is even more primitive than the matter found in primitive Solar System bodies. Additionally, a tentative dependence on the irradiation temperatures was seen in the G band properties.