It looks like there's no direct evidence from any pre-Neolithic culture about their sexual or marital arrangements. However, the proxy evidence is a bit more extensive:
In a comparative study of 190 hunter-gatherer societies, Apostolou [11] showed that arrangement of marriage by parents or close kin is the primary mode of marriage in 85% of the sample; brideservice, brideprice, or some type of exchange between families is found in 80% of the sample; and less than 20% of men are married polygynously in 87% of the sample. [...]
The reconstruction of low levels of polygyny in early humans is straightforward because high levels of polygyny for hunter-gatherers are only found in Australian Aborigines and are mostly low elsewhere (most exceptions are some New World foragers that are not in the phylogenetic analysis). Low levels of polygyny and low reproductive skew among ancestral humans are consistent with human morphology and behavior (i.e., moderate sperm counts [20] and testicular size [21]; facultative paternal investment [22]) and the general decline in sexual dimorphism beginning at least with early Homo [23].
And yes, there is a contrary opinion, [at least on the last matter, dimorhpism] as with all such issues:
However, human sex differences in size underestimate sex differences in the traits most relevant to contests. This is partly because women are unique among primates in having copious fat stores (Pond & Mattacks, 1987), perhaps for building the large, fatty brains of human offspring (Lassek & Gaulin, 2008), and as sexual ornamentation (see below). When fat-free mass is considered, men are 40% heavier (Lassek and Gaulin, 2009, Mayhew and Salm, 1990) and have 60% more total lean muscle mass than women. Men have 80% greater arm muscle mass and 50% more lower body muscle mass (Abe, Kearns, & Fukunaga, 2003). Lassek and Gaulin (2009)) note that the sex difference in upper-body muscle mass in humans is similar to the sex difference in fat-free mass in gorillas (Zihlman & MacFarland, 2000), the most sexually dimorphic of all living primates.
In fact it goes on for almost a full page just on this, which I won't fully reproduce here.
And if you like this line of argument, David Barash has a whole book about it "Out of Eden: The surprising consequences of polygamy" (OUP, 2016). However, I'll note/quote from a long review of that book that
he argues
that female choice could drive the evolution of male violence in these situations by
women choosing violent men to protect them (p. 72ff). However, there is little or no
evidence that this is what women have been or are doing, and certainly no evidence
that this is what women (or men) did in ancient communities not subject to serious
resource pressures.
Which basically gets back to what I said in the beginning of my answer: no direct evidence either way.
And to mention molecular genetics, Hammer (2008) has argued that polygyny is found by looking at the diversity of the Y-chromosome vs that of the X-chromosome. However, this view was later challenged by alternative explanations by Sayres (2014) of the low diversity of the Y-chromosome, in particular background selection.
Likewise, the data that Favre and Sornette (2012) (pointed out in the comments below) based their conclusions on
The Time to the Most Recent Common Ancestor (TMRCA) based on human mitochondrial DNA (mtDNA) is estimated to be twice that based on the non-recombining part of the Y chromosome (NRY).
was refuted merely a year later by new data, Poznik 2013
Applying equivalent methodologies to the Y and mtDNA, we estimate the time to the most recent common ancestor (TMRCA) of the Y chromosome to be 120–156 thousand years and the mtDNA TMRCA to be 99–148 ky. Our findings suggest that, contrary to prior claims, male lineages do not coalesce significantly more recently than female lineages.
If you want some genetics-based insight that hasn't yet been proven wrong, a 2015 paper, Karmin et al., says
In contrast to demographic reconstructions based on mtDNA, we infer a second strong bottleneck in Y-chromosome lineages dating to the last 10 ky. We hypothesize that this bottleneck is caused by cultural changes affecting variance of reproductive success among males.
Which they interpret more explicitly as:
the drop of the male Ne [effective population size] during the mid-Holocene corresponds to a change in the archaeological record characterized by the spread of Neolithic cultures, demographic changes, as well as shifts in social behavior.
And contrary to what is claimed in the comments below, but also contradicting Sayres (2014) [not on the plausibility, but on the factuality of the non-demographic explanations], Poznik et al. 2016 (to which Sayres is a co-author) say that demographic bottlenecks in the last few thousand years are enough explanation:
We confirmed that Y-chromosome diversity in our sample was low
(Supplementary Fig. 24) and found that positing extreme male specific
bottlenecks in the last few millennia could lead to a good fit
between modeled and observed relative diversity levels for the autosomes,
X chromosome, Y chromosome, and mtDNA (Supplementary
Figs. 25–28, Supplementary Table 16, and Supplementary Note). Therefore, we conclude that Y-chromosome diversity may be shaped
primarily by neutral demographic processes.
So no need for very ancient polygyny (pre-Neolithic) to explain the genetics observed on the Y-chromosome. (Also note that the supplementary material for this paper is over 100 pages long!) Of course, by next year some of this will probably be outdated, such is the nature of fast moving field.
