Humans have high lactase at birth but it was a mutation in a lactase-production allele that permanently jammed it "on" for some part of the population.

> it’s unlikely you could trace the mutation back to one person.

But that's how allele mutations work, mostly. Unless you think genetic drift could cause it in a lot of people in a very short period, which AFAIK is considered unlikely. Instead a lot of baby-making was involved.

From The evolution of lactase persistence in Europe. A synthesis of archaeological and genetic evidence:

> LP [lactase persistence] is an autosomal dominant trait (Enattah et al., 2002). Lactase production is genetically determined by a single gene, LCT, located on chromosome 2

> using long-range haplotype conservation (Bersaglieri et al., 2004) and variation in closely linked microsatellites (Coelho et al., 2005), the 13,910*T variant has been estimated to be between 2188 and 20,650 years old and between 7450 and 12,300 years old, respectively.

> This dramatic change of LP frequency in a relatively short time span cannot be explained by genetic drift alone; very strong natural selection needs to be invoked.

http://www.uni-mainz.de/FB/Biologie/Anthropologie/MolA/Downl...

Do note that the article there discusses different mechanisms for lactose persistence occurring in different populations (quite explicit in 5.3).