Recently these and other questions suggest we should look far back into the record of mammals on earth, to study the evolution of life as we know it, and especially the relationship between humans and food -- since food nearly always tops the list of factors that could lead to early menarche.
Here we have a time line that challenges us to realize the vast history we may have to study.
We see here at 200,000,000 years ago, the co-evolution of plants and mammals, beginning with the appearance of angiosperm, plants reproducing through flowers and fruits (nuts and seeds).
Recently the earliest being that can be related to the line leading to humans has been found. It would have weighed about 2 grams, was the size of a paperclip but relatively had the big brain we have in our line (ref: Science 2001)