Throughout its ancient and modern history, cosmology employed the most sophisticated mathematical apparatus and calculations, and the best available, advanced and expensive technologies of observations and instruments. Despite or because of all this, it also always involved metaphysical beliefs, wishful thinking and fundamental assumptions that, due to their generality and hypothetical extrapolations could never be fully verified. The above is also true, if less frequently discussed, of our current, generally accepted relativistic cosmological theory of the Big Bang. Its first versions appeared in the 1920s, but encountered strong resistance and took more than 40 years to gain gradual, step-by-step recognition. Einstein’s theory of gravitation remained a hugely respected theory even when the number of active researchers in the field was quite small. But for many practicing physicists and astronomers, the cosmological extrapolation of general relativity appeared too speculative and dubiously scientific. This presentation will discuss the sources of those critiques and the convergence of arguments and factors – technological, observational, socio-political, and existential – which circa 1960 led the sea change in attitudes and to the widespread acceptance of Big Bang theory as a highly prestigious and popular area of research in fundamental physics, and the scientific basis for our current cosmological worldviews and further speculations.