The variant wouldn't have been there if the mutation had not happened. No black moths were seen in the 1811 observations or before. By mid-1800s the population was riddled with them and by the end of the century it was the norm in the population.
I suspect PaulK is correct. Such melanin mutations are not rare and could have come and gone several times in a large population over many centuries. So you are correct. This one crept up just in time (+-40 years)
So your definition of change is more moving things around than creating something new? And yet you acknowledge that mutations, like SNPs, do happen. A single SNP would make a change. Make something new. Yes?