This article investigates the potential of persistent homology for constraining cosmological parameters and primordial non-Gaussianity amplitudes.Persistent homology using persistence images (PIs) performs better than the combined Power Spectrum and Bispectrum (PS/BS) for inferring parameters.PIs show promise in constraining primordial non-Gaussianity, particularly for the parameter fNL^loc.The combination of PIs with PS/BS provides only marginal gains, indicating little extra information in PS/BS compared to PIs.