The cosmic neutrino flux recently discovered by IceCube will be instrumental in probing the highestenergy astrophysical processes. Nevertheless, the origin of these neutrinos is still unknown. While it would be more straightforward to identify a transient, or galactic source, class, finding a population of distant, continuous sources is challenging. We introduce a source-type classification technique that incorporates all available information from catalogs of source candidates. We show that IceCube-Gen2 can statistically establish the origin of cosmic neutrinos, even for the most challenging source populations-starburst galaxies, AGN, or galaxy clusters-if neutrino track directions can be reconstructed with a precision similar to 0.3 degrees. We further show that the source catalog out to similar to 100 Mpc can be sufficient for the most challenging source types, allowing formore straightforward source surveys. We also characterize the role of detector properties, namely angular resolution, size, and veto power in order to understand the effects of IceCube-Gen2's design specifics.