What has been proved about the big bang, and what has not? Ok so the universe is in constant expansion, that has been proven, right? And that means that it was smaller in the past.. But what's the smallest size we can be sure the universe has ever had?
I just want to know what's the oldest thing we are sure about.
 A: Spencer's comment is right: we never "prove" anything in science. This may sound like a minor point, but it's worth being careful about.
I might rephrase the question like this: What's the smallest size of the Universe for which we have substantial observational evidence in support of the standard big-bang picture?
People can disagree about what constitutes substantial evidence, but I'll nominate the epoch of nucleosynthesis as an answer to this question. This is the time when deuterium, helium, and lithium nuclei were formed via fusion in the early Universe. The observed abundances of those elements match the predictions of the theory, which is evidence that the theory works all the way back to that time.
The epoch of nucleosynthesis corresponds to a redshift of about $z=10^9$. The redshift (actually $1+z$) is just the factor by which the Universe has expanded in linear scale since the time in question, so nucleosynthesis occurred when the Universe was about a billion times smaller than it is today. The age of the Universe (according to the standard model) at that time was about one minute.
Other people may nominate different epochs for the title of "earliest epoch we are reasonably sure about." Even a hardened skeptic shouldn't go any later than the time of formation of the microwave background ($z=1100$, $t=400,000$ years). In the other direction, even the most credulous person shouldn't go any earlier than the time of electroweak symmetry breaking ($z=10^{15}$, $t=10^{-12}$ s.)
I vote for the nucleosynthesis epoch because I think it's the earliest period for which we have reliable astrophysical evidence. 
The nucleosynthesis evidence was controversial as recently as about 10 or 15 years ago, but I don't think it is anymore. One way to think about it is that the theory of big-bang nucleosynthesis depends on essentially one parameter, namely the baryon density. If you use the nucleosynthesis observations to "measure" that parameter, you get the same answer as is obtained by quite a variety of other techniques.
The argument for an earlier epoch such as electroweak symmetry breaking is that we think we have a good understanding of the fundamental physical laws up to that energy scale. That's true, but we don't have direct observational tests of the cosmological application of those laws. I'd be very surprised if our standard theory turns out to be wrong on those scales, but we haven't tested it back to those times as directly as we've tested things back to nucleosynthesis.
A: For an alternate answer, consider the inflationary universe. (Look up Inflation (Cosmolgy) in Wikipedia.)
Cosmologists say we have substantial evidence for inflation.  The time of inflation is somewhat uncertain, but with high probability it is very early, if it occurred at all.  Wikipedia says 10^-36 to 10^-32 seconds. 
A: BBT is not proved and it can not be proved, and I point in this answer to a new model that will knock it down.
While a physical law was never broken, and is expected to be unbreakable; a theory come and go as time goes by.  
In the begining of BBT (Big Bang Theory) it was expected that gravity will, in due time, make the universe to collapse. A few years ago, against the expectations, it was measured an acceleration of the expansion.
Because the matter content of Universe is not working to bring an end to the expansion we can deduce that Bariogenesis can not be an argument in favor of BBT (matter plays a minor role).  
The cosmological constant and the Dark Energy appeared magically to explain the feature, without explaining. Its only a parameter inserted in the equations, and proceed as usual.   
To explain the observed, i.e. measured, expansion of the space we have to consider what stands behind 'making a measure', what referential can we chose, etc,... and one have to search for more than the naive explanation that you know of.   
ΛCDM model (BBT) has 6 parameters: H0 , w, ΩΛ , ΩM , ΩR and ΩK   
You can find here a killing theory with only one parameter (H0); this paper was dated July 1, 2011 and submitted to PRX; it is easy reading and any undergrad student can understand it. It is my hope that the teachers will follow. I'm very proud to see my name in this foundational paper, and I will stand up to argue in favor of it.  
A self-similar model of the Universe unveils the nature of dark energy 
The abstract  

This work presents a critical yet
  previously unnoticed property of the
  units of some constants, able of
  supporting a new, self-similar, model
  of the universe. This model displays a
  variation of scale with invariance of
  dimensionless parameters, a
  characteristic of self-similar
  phenomena displayed by cosmic data.
  The model is deducted from two
  observational results (expansion of
  space and invariance of constants) and
  has just one parameter, the Hubble
  parameter. Somewhat surprisingly,
  classic physical laws hold both in
  standard and comoving units, except
  for a small new term in the angular
  momentum law that is beyond present
  possibilities of direct measurement.
  In spite of having just one parameter,
  the model is as successful as the ΛCDM
  model in the classic cosmic tests, and
  a value of H0 = 64 km s−1 Mpc−1 is
  obtained from the fitting with
  supernovae Ia data from Union
  compilation. It is shown that in
  standard units the model corresponds
  to Big Bang cosmologies, namely to the
  ΛCDM model, unveiling what dark energy
  stands for. This scaling (dilation)
  model is a one-parameter model that
  seems able of fitting cosmic data,
  that does not conflict with
  fundamental physical laws and that is
  not dependent on hypotheses, being
  straightforwardly deducted from the
  two observational results above
  mentioned.

I will try to explain this novel theory in a few words:
All system of units we use are 'atomic units' because are based in the properties of the atoms around us. And we only knew how to apply the laws of nature if we use those units.
We are 'anthropocentric' and we can only imagine that the atom is absolute, invariant in time. Yes, we are using an 'absolute reference' and also denying that an 'absolute reference' can exist.  
A measure is an adimensional quantity, a ratio of two quantities: e.g. if we are measuring a distance in the numerator is the amount of length and in the divisor is the amount corresponding to the unit of measure.
As we are measuring an expansion we have to consider : the space expands, the unit of measure is decreasing (our atom) or a mix of both.  
In the paper it is shown that the laws of nature can support a scaling property of the universe, where the atom is no more invariant. It is shown that by choosing a  proper referential, a comoving one, the dark energy and the cosmological constant are artifacts of BBT. The BB is no more needed; the Inflation era is no more needed, etc.  
The unexpected: (quote)   

Atomic measures are number counts
  We will now see that the measures of
  bodies’ properties using atomic units
  are independent of the base quantities
  and dependent on the number of
  particles or atoms.

