Most anthropologists attach the rise in patriarchy to agricultural forms of subsistence (which arose at about the same time as monotheism in the middle east, but the male "lord god" is more of a symptom of this than the cause.) Patriarchy is also a common social form in nomadic herding cultures (also a predominant form of subsistence in the Mid East & North Africa.)
Horticultural societies, in contrast, almost exclusively relied in matrilineal, and matriarchal structures. All land inheritance, and therefore social power was passed from mother to daughter.
Foraging (Hunter/Gatherer) societies tend to be mixed with equitable power distributions. In fact one of the most enjoyable and fascinating aspects is how incredibly plastic gender taboos & rolls tend to be in these small scale nomadic societies. For instance in Sioux tribes in North America entering the roll of "two spirit" (what we would call transgender) was considered to be a rare, and sacred aspect. A person could essentially elect to live out their lives as the other gender. There are many many other examples of such social accommodations to the myriad of ways a people can want to live outside their born gender.
The male "lord god" is definitely a symptom of patriarchy. However the cause has been correlated with Agricultural forms of subsistence. Agriculture brought the home away from the center of society (political and economic) for most individuals (remember +90% of people were farmers pre-industrial revolution.) The societies you mention are all agricultural, save the Pacific Islands since there continue to be thousands of unique cultures in the region so I would ask you to be more specific before I could respond to that.
Let me offer an explanation of why agriculture has lead to wide spread patriarchy:
Since women's roles are greatly tied to the children their care and subsequently where they can be cared for( the home) women were removed from the center of society by the need to remain with the homestead. Men, by contrast continued in their rolls as the individual who roams far from home in order to provide (historically both hunters herders are male dominated roles to an extreme degree.)
Through this stark division, men became the holder of social power & women lost so much power it was common to see them not as partners but property. Examples of being considered property are foot binding, genital cutting/mutilation, and loss of rights to property and legal recourse against husbands and male family members.
Agriculture is a means of production which produced large, dominating, societies due to the ability of the culture to produce enough food to sustain cities, armies, and other specialist trades which would then produce better weapons & technology to further the society's influence and power. It is for this reason that we see so many contemporary societies with cities/states and also patriarchal roots. They've simply wiped out or absorbed their neighbors since the dawn of agriculture 7000 years ago.
Hunting-gathering tribes could support 1 small child per woman because the woman had to carry him / her.
Agricultural societies could support more children, thus they out-competed hunting-gathering ones.
More children --> women spend more time on childcare, at home etc.
I think is a large part of why such societies expanded. Certainly societies depending entirely on natural cycles are more directly subject to the natural laws governing overpopulation. Agriculture requires each individual to do much more work per day, but produces an exorbitant amount of food, enough to sustain an aristocracy and thousands of other professions which have no independent means of feeding themselves or their families.
Something else worth noting is that a woman who is living the incredibly active lifestyle of a forager while also eating the low fat, grain free diet is fertile less of the time (especially while lactating, a process that would continue until her child was 2 or more, limiting the number of children born overall.)