Again, the big bang theory, which has stood the test of time, rests on two theoretical pillars: general relativity and the cosmological principle. Space/time is finite, it had a real beginning, it expands and indeed as you say it is accelerating:
The temperature is uniform to better than one part in a thousand! This uniformity is one compelling reason to interpret the radiation as remnant heat from the Big Bang; it would be very difficult to imagine a local source of radiation that was this uniform. In fact, many scientists have tried to devise alternative explanations for the source of this radiation but none have succeeded.
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One of the profound observations of the 20th century is that the universe is expanding. This expansion implies the universe was smaller, denser and hotter in the distant past. When the visible universe was half its present size, the density of matter was eight times higher and the cosmic microwave background was twice as hot. When the visible universe was one hundredth of its present size, the cosmic microwave background was a hundred times hotter (273 degrees above absolute zero or 32 degrees Fahrenheit, the temperature at which water freezes to form ice on the Earth's surface). In addition to this cosmic microwave background radiation, the early universe was filled with hot hydrogen gas with a density of about 1000 atoms per cubic centimeter. When the visible universe was only one hundred millionth its present size, its temperature was 273 million degrees above absolute zero and the density of matter was comparable to the density of air at the Earth's surface. At these high temperatures, the hydrogen was completely ionized into free protons and electrons.
Since the universe was so very hot through most of its early history, there were no atoms in the early universe, only free electrons and nuclei. (Nuclei are made of neutrons and protons). The cosmic microwave background photons easily scatter off of electrons. Thus, photons wandered through the early universe, just as optical light wanders through a dense fog. This process of multiple scattering produces what is called a thermal or blackbody spectrum of photons. According to the Big Bang theory, the frequency spectrum of the CMB should have this blackbody form. This was indeed measured with tremendous accuracy by the FIRAS experiment on NASA's COBE satellite.
Eternal cosmologies need not assume a first cause or accident, but they shift the burden of explanation into the infinite past. Although every event might be explicable by earlier events and causal laws, eternal cosmologies cannot even address why a temporally infinite cosmos exists and why it is the way it is. And there might be even deeper problems. Because we are able to assign a symbol to represent 'infinity' and can manipulate such a symbol according to specified rules, one might assume that corresponding infinite entities (e.g. particles or universes) exist. But the actual (i.e. realized in contrast to potential or conceptual) physical (in contrast to the mathematical) infinite has been criticized vehemently, being non constructible, implying contradictions, etc. (cf Hilbert 1964, p. 136, Spitzer 2000, Stoeger, Ellis & Kirchner 2004, ch 5). If this would be correct it should also apply to an infinite past. (A future-eternal cosmos might be less problematic if it is viewed as an unfolding, unbounded, i.e. only potential one.) This is a controversial issue, but it might be seen as another motivation to search for alternatives to past-eternal cosmologies.
Initial cosmologies, on the other hand, run into deep metaphysical troubles to explain how something could come out of nothing and why there is something rather than nothing at all (cf. Nozick 1981). Even the theological doctrine of creatio ex nihilo does not start with nothing but at all but with something that is God, so the principle "ex nihilo nihil fit" still holds.
You are correct, that an expanding universe is evidence of a smaller universe in the past, ultimately pointing to a singularity or possibly multiple singularities (big bangs) as Hawkings has hypothesized.
There are a couple of flies in the ointment though. The first is that the growth of the Universe is accelerating. The second is that dark matter/energy theories are necessary to explain the big bang.
Just like the Theory of Evolution is silent on the origin of life, Physics doesn't have an explanation for the origin, if there was an origin, of the universe. We are like babes opening our eyes to the wonders before us : )
One thing we can be sure of though, is that Despator didn't make it : )
That is correct, but not all evidence is to the contrary. The accelerating expansion has everyone baffled. If it isn't a steady state, all bets are off.