Depends what you mean by "objective happiness". If we use the term in the way that it's used by Kahneman etc., meaning that
In the special conditions of the clinic or laboratory it is sometimes possible to obtain continuous or almost continuous reports of experienced utility from patients or experimental subjects. Continuous measures are of course impractical for the measurement of objective happiness over a period of time. Sampling techniques must be used to obtain a set of values of moment-utility that adequately represents the intended population of individuals, times and occasions. For example, a study of the objective happiness of Californians should use a sample of observations that reflects the relative amounts of time spent on the freeway and in hot tubs. Techniques for sampling times and occasions have been developed in the context of Experience Sampling Methodology (ESM) (Csikszentmihalyi, 1990; Stone, Shiffman and DeVries, 1999).
It's hard to imagine getting such data retrospectively from ancient or even just past populations.
Ref quoted: Kahneman, D. (2000). Experienced utility and objective happiness: A moment-based approach. In D. Kahneman & A. Tversky (Eds.), Choices, values and frames (pp. 673-692). New York: Cambridge. University Press and the Russell Sage Foundation.
Generally, diet and/or physical trauma leave a bone recod for archeologists to study. Alas I'm not aware of neurochemistry of past populations being ammenable to study (other than comparative studies across current species, e.g. humans vs apes).