How do these observations provide evidence that supports the Big Bang Theory?

Let's think this through:
"Big Bang" is implied by
"Receding Galaxies", which are implied by
"Doppler Effect", which is caused by
"Motion Away From Us", which is assumed from
"Red Shifted Light"

So we have this remarkable train of logic all based on a single phenomenon and an assumption. If that assumption is wrong then most of what we think we know about the universe ain't so. Well, Doppler effect is not the only cause of red shift. So there you are: guesses offered in lieu of actual science.

Greatest Mysteries of Cosmology
http://www.science-frontiers.com/sf138/sf138p02.htm

"Redshift is A Shaky Measuring Rod"
http://www.science-frontiers.com/sf138/sf138p03.htm