How does the red shift support the Big Bang theory?

when we observed stars from the Earth, we noticed that almost all of the light emitting from the stars was being shifted to the red end of the spectrum. This indicates that the wave was essentially being 'stretched' from our perspective. From these observations we can deduce that the stars are moving away from us, and we can extrapolate that data to assume that at some point in the distant past all matter would have had to originate from a single point. What we then needed an answer for was what caused the matter to come into existence and start expanding at a rapid rate. This ids what we call the Big Bang theory.