Big Bang cosmology arose originally from two bodies of evidence:
a) As observed from our position, all objects beyond the Local Group of galaxies exhibit a spectral red shift that increases in direct proportion to distance. This is interpreted in all cases as a function of the doppler effect, indicating motion away from us at speeds that increase with distance, hence expansion of the universe. The expansion is extrapolated backwards all the way to an initial pinprick.
b) The universe has a consistent background temperature in all directions, which is interpreted as the remnant of an initial expansion, and some of the predictions for the patterns in that radiation based in Big Bang theory appear to be confirmed by surveys such as COBE.
At the same time, because of the size of the observable universe as opposed to its posited age, Big Bang theory currently requires a hyperinflationary period of expansion that is entirely theoretical. I think that's too many extrapolations to justify the certainty of modern cosmologists. In sociological terms, it looks suspiciously like the certainty of all prior scholastics, whose world-views arose and were taken as axiomatic and unchallengeable until they were overthrown (usually after the reactionary last stand of "adding epicycles" - hyperinflation, anyone? - and holding Inquisitions in defense of the reigning paradigm).
I don't think the evidence given for Big Bang is enough for basing a cosmology that incidentally also meets our human craving for a convenient story with a beginning and an end, and even matches the Genesis god's proclamation of "Let there be light." Both the red shift and the background radiation can have other causes. I do think the data base underlying psychology and sociology is sufficient to allow us to consider the hypothesis that present-day cosmologists are involved in wishful group think, like so many groups of scholars dealing with the unknown in the past.
If cosmology is based on too little available data, I submit a dominant theory is not better than an admission of ignorance. But the lack of a dominant theory in cosmology would be a social ill among scientists, who will look down on a discipline that lacks ones, and even more so among the funders of science, who want their money to pay for concrete findings. Historically we have seen how every picture of the universe until now turned out to be based on what we could see within a horizon that always proved to be limited. Each dominant paradigm fell as each horizon was exploded by subsequent observation. Today we look out in all directions and see a similar picture of the universe at similar distances, seeing no further in any direction than in any other, all of which implies that we are once again seeing a horizon, even if its scale seems incomprehensibly huge. We don't know the actual size or structure of the universe because we have no idea what lies beyond that horizon, and have no basis for making assumptions of isotropy (similarity regardless of direction), homogeneity (similar in all parts), or a Copernican principle (no center), all of which are vital to present-day Big Bang theory.
Galaxies don't seem to have enough mass visible to us to explain the maintenance of their structure by way of gravity, so we posit that 90 percent of the mass consists of dark matter. (Translation: We don't know.) The apparent expansion of the universe seems to be accelerating faster than we can explain, so we posit that 90 percent or more of the energy is also dark. (Translation: We don't know.) Why are these speculative entities superior to assuming forces or structures we have yet to discover? We get radically different pictures of our cosmic neighborhood depending on the wavelength of the radiation we observe, again implying that we are simply not observing a significant percentage of the whole (like the parable of the blind men and the elephant). We discover awesomely large galactic agglomerations that may be the product of larger structures or processes we have yet to see or conceive.
The paucity of the empirical evidence for present-day cosmology is well-covered in this excellent and readable article by astronomer M.J. Disney:
http://nedwww.ipac.caltech.edu/level5/Disney/Disney_con... THE CASE AGAINST COSMOLOGY
M. J. Disney
Physics and Astronomy, Cardiff University, Cardiff CF24 3YB, Wales, UK
"Abstract. It is argued that some of the recent claims for cosmology are grossly overblown. Cosmology rests on a very small database: it suffers from many fundamental difficulties as a science (if it is a science at all) whilst observations of distant phenomena are difficult to make and harder to interpret. It is suggested that cosmological inferences should be tentatively made and sceptically received."
I cringe when I hear Big Bang theory described as cosmology's pendant to evolutionary theory in biology. The two are simply not comparable. We are present on the planet on which evolution occurred, whereas all we know about the rest of the universe is what the observable radiation tells us. We can see evolution and the mechanism of selection in present-day action, trace evolutionary history through a rich and relatively complete record, and study its issue (life) on all levels: biotope, species and niche, organism and biochemistry, molecular chemistry. Of the stars all we have is what we can deduce from the light that reaches us. Cosmology as it currently stands is a faith.