"There is genetic evidence that we are descendants from the same ancestors as primates."
Which is based on assumptions used to support that apes and men evolved from a common ancestor. Now, this is putting the cart before the horse since there is no empirical evidence to back up the theory of evolution. We can test gravity, fusion, and fission; we can observe and measure redshift and other cosmological data that is used to support the theory of the decay of the speed of light. In fact it is the observed redshift data that has led some cosmologists and physicists to question that the speed of light has been constant since the "Big Bang".
Now if light speed has decayed then the time necessary for evolution, which theorizes billions of years then evolution falls on observed and tested (empirical) scientific evidence.
Theories come and go. Aristotle believed light speed was infinite, a belief held by scientists until 50 years after Olaf Roemer's test results determined the speed of light can be measured.
You want others and me to accept evolution as a viable theory and explanation for the origins of life then trot out the empirical evidence (not theorized and intepreted evidence) that apes and man evolved from a common ancestor.