What is one piece of evidence that does NOT support the Big Bang Theory?

The redshift data does not support the Big Bang Theory and  without the redshift interpretation favored by the Big bang, there is  no Big Bang.  

Edwin Hubble did not believe that the redshift indicated  expansion. Hubble saw the redshift as an hitherto unrecognized  principle of nature.  The redshift is the effect of centripetal force mv2/r = mv2/ct =  v/c(mv/t) = v/c(p/t)= (v/c)m

The unrecognized principle of nature is the refraction effect of  gravity on light.  

n=c/v or v= c/n.

The Universe is older than 13.7 Billion years, likely around  16.5 billion years.  

The proper law of Gravity is W = -mGM/r + cmV = -mu/r + cP where  cP is the so-called "Dark Energy", or the actual vector Momentum  Energy cmV= cP. This is The Quaternion Universe with scalar and  vector energy!

Hope this helps!

luster is not a good characteristic to use by itself because luster is the property of minerals that indicates how much the surface of a mineral reflects light. the luster of a mineral is affected by the brilliance of the light used to observe the mineral surface.

e/c, where e is its total energy