We investigate inclusive forward single-hadron production in high-energy proton–proton collisions using a CGC-inspired Monte Carlo event generator, MC-CGC. We carried out a systematic study of the sensitivity of the running-coupling Balitsky–Kovchegov (rcBK) evolution equation to its initial conditions by comparing three parameterizations: the McLerran–Venugopalan (MV) model and its two HERA DIS-constrained variants, MVand MV. Our results indicate that the current LHCb data favor the MVand MVmodels, while the differences from the original MV model become more pronounced at higher transverse momentum and at mid-rapidity. As a complementary analysis, we also compared the dilute–dense (DHJ factorization) and dense–dense (k_T factorization) frameworks. We found that the k_T factorization framework provides a better description of the particle production spectra at mid-rapidity than the DHJ framework, where both the projectile and target are in the dense regime at LHC energies. Predictions for the FoCal measurements at ALICE, including the production of identified neutral mesons and jets, are also presented.