RiseAgainst said:
What real proof is there of the Big Bang? I have never heard anything that is convincing. And how do scientists determine the age of the universe, is it really calculated or is it just estimated?
Welcome to PF, RiseAgainst!
I do not know how much formal training you have had, in science, nor to what level, so the following may be far to simplistic (please let me know if it is).
First, in modern science, we don't talk about "real proof" - that's something only possible in mathematics - rather we use 'consistency'.
For example, we can say that all experiments conducted, and observations made, here on Earth, and in our solar system, are consistent with (Einstein's) General theory of Relativity (GR). We can also say that GR has no internal inconsistencies - its logic is sound and the mathematics it is built with well-established (and, in this case, proven).
Second, the term 'the Big Bang' is not used by the scientists who study this branch of astrophysics (cosmologists); rather there are a number of models whose scopes (or domains of applicability) are clearly stated and limited. Perhaps the most widely studied model* is the LCDM one, which is based on GR and the Standard Model (of particle physics) plus "Lambda" and "Cold Dark Matter".
There are 'three pillars' to support the LCDM model; that is three sets of independent observations (or phenomena) which can be fully explained by the model (or, saying this another way, the LCDM model is consistent with all relevant observations in these there sets): the Hubble relationship, the primordial abundance of light nuclides, and the Cosmic Microwave Background (CMB).
Each of these sets of observations is quite extensive, comprising millions, or billions, of individual datapoints, and each has been reported in (collectively) thousands of papers published in scientific journals. The science behind the observations, and their analyses, has been intensely scrutinised, challenged, argued over, and generally put through the wringer ... over the past many decades, so each observational pillar is extremely solid.
It is very important to keep in mind that LCDM models say nothing whatsoever about the origin of the universe; in fact, their domains of applicability go only to when the universe was extremely hot and dense - as hot and dense as the collisions in the most energetic of particle physicists' colliders - and no further (though there are other cosmological models whose domains of applicability do go beyond this).
If you don't find this convincing - and I expect that you may not - please ask more questions!
I'll leave the question of the estimated age of the universe to a later post.
*
it's actually a class of models