But don’t you need to know what color it was to begin with?
We are talking about a galaxy as it existed over 11 billion years ago, less than 3 billion years after the universe first formed. The composition of that galaxy, including the number of red, yellow and blue stars, would affect the red/blue spectrum at the source, throwing off the baseline assumptions being made to calculate the velocity using the Doppler effect.
It seems like a lot of guesswork to me.
It’s a little more complicated than just using the wavelength of light, since there is no way to tell for certain what it started as. Spectral signatures of elements like hydrogen and oxygen form the criterion for measuring the Doppler shift, since their absorption and emission spectra are always the same, so we assume. Fortunately, it’s easy to identify elements using their spectra from any distance across the universe.