Problems with the steady state theory began to emerge in the late 1960s, when evidence started to show that the universe was in fact changing: quasars and radio galaxies were found only at large distances (and thus, because of the finiteness of the speed of light, in the past), not in closer galaxies. The final blow came with the discovery of the cosmic background radiation in 1965 which was predicted by the big bang theory, and not the steady state theory.
Today, the big bang theory is the one that astronomers consider a good approximation to describing the origin of the universe and the basis of more complete theories.
Observational cosmologists deal with observations, and because the universe and the speed of light are both finite, one can only observe data within a sphere centered on the observers. What is outside that sphere is therefore not accessible to observational cosmologists.
Theoretical cosmologists regard the big bang model as incomplete in part because it does not address the issue of what happened before the big bang. Some of these speculations about what happened before the big bang (and what would happen after the Big Crunch) are qualitatively somewhat similar to the quasi-steady-state model.