This is not possible because mutant number one would be alone in the world. Let say the first paleo human mutant(the missing link as it were) had a skull, nose and brow like a modern human. Well to ALL the others big browed, nosed, and low skulled humans, that would be a very undesirable mate, looking different. The suddenly appears thing does not work
It happens by degrees, but the advantage can be hidden, or cumulative. Also could coincidentally make one more attractive, but that’s not really that relevant. The gene would be carried into the next generations, where other factors would predominate and favor or not favor the gene.