The widely heralded, remarkable, progress in cosmology leading to the emergence of a 'standard cosmological model’ has relied on certain key assumptions at different levels. I describe works along multiple facets from the research program of my group at IUCAA over the past 15 years, that have all attempted to adopt an agnostic approach in drawing cosmological inference independent of such assumptions, in the context of the increasing exquisite observations of the Cosmic Microwave Background CMB anisotropy.