I agree in general with what hellfire says here, and have some extra detail to add.
FeynmanMH42 said:
"did the Universe, time, space and the whole whatevery actually begin with the Big Bang?" or "there is no scientific evidence the Big Bang was the beginning of the Universe, why should we believe it?" ...
there is no scientific reason to believe it.
you can believe it if it makes you feel good, or fits in nice with your religion or your aesthetic ideas of what ought to be
I stick very close to mainstream cosmology---not attracted by fringe ideas.
Mainstream cosmo has accumulated a magnificent bunch of data of many kinds. Two models fit equally well, classic GR and LQC---that is, the current consensus model LambdaCDM can be based either on classic GR or on LQC.
Both basis theories provide you with the Friedmann equation that you need, the only difference is that one version is quantized and the other isnt.
The unquantized (classic) model breaks down at the start of expansion. The quantiized model (LQC basis) does not break down and continues back into the past before the start of expansion.
The LQC version is so far indistinguishable from classic GR in what it says about what we observe because to a close approximation it DUPLICATES classic GR as soon as a few Planck units of time have passed after the start of expansion. The convergence to the classic theory as a limit is very fast.
However there are some differences which may afford the opportunity to distinguish between the two in the future. There was a recent article by Magueijo and Singh about that. (The quantized version does not have a "horizon problem"---which was what motivated people to invent "inflation" scenarios---so it appears that inflation is simply an option. Differences in structure formation may show up. Currently, no available data can distinguish between the two, but future observations are expected to.)
At present there is no scientific reason to prefer one version to the other. since only the classic version breaks down, there is no scientific reason to prefer a breakdown at the start of expansion.
=====================
BTW the success of LQC in achieving this has only been completed in the past 2 years. It has NOT been paralleled by developments in string theory (ekpyrotic model is more speculative and does not as yet give a deterministic evolution thru the big bang moment).
However string-based cosmology COULD catch up---it simply has not so far. It would have to reproduce the classic Friedmann equation, which hasnt happened as yet in the string context.
Since these developments (associated with new LQC dynamics, 2005 and 2006) are recent, not everybody knows about them.
So you won't get exactly this story (some people will discuss it as if string cosmology and loop cosmology were about on par, which at present they are not).