You got that right: bigbang is based on red-shift, i.e., galaxies appear redder than they ought to, which would indicate they are receding from our perspective. “Redder than they ‘ought’ to be”? In whose lexicon?
The premise was, when I read it in 1963, that the assumption was, that the most prevalent metallic element in all galaxies ought to be, iron; therefore, its characteristic orange-ish glow should be orange-ish; but in distant galaxies, the glow was redder than that, hence those galaxies (by Doppler-ish contexts) must be receding, hence an expanding universe, hence, there must have been an initial point, hence, big bang.
Critical variable, unexplained yet assumed, who says galaxies should glow one color or another?
It's clear you don't know anything about physics. Look up 'Lyman Alpha Line' and get back to me. Light from stars has distinctive spectral lines that are still obvious even when red-shifted.