I suppose to most people primogeniture looks like a fairly obvious thing, but there are a number of other ways in which power could be inherited. In the Near East ultimogeniture (inheritance by the youngest) seems to have been practiced. At the least there are a number of hints in the Old Testament that it occurred. And the Minoans/Mycenaeans seem to have had a strong cultural tie to the Near East. There may also be hints of ultimogeniture in a number of European folktales, though that may stem from something other than actual practice. OTOH, it may be significant that both Zeus and Uranus were youngest sons.

Another possibility may have been some sort of elective kingship, priesthood, etc. with the candidates drawn from within a given family. This was practiced by several later IE cultures such as the Celts and some of the Germanic tribes.

And then we also had a discussion a few years ago about the possibility of a matrilineal succession, with the kingship going to the husband of the woman who bore the royal right. That does, however, leave open the question of which daughter it was who bore that right.

Any of these would fit just as well into a highly structured system as primogeniture would. But was the system that rigid and highly structured? Certainly the records we have make it seem so, almost more so than the Dominate of the fifth century AD. But records can be deceiving and we have a very narrow sample. Maybe the records we have only reflect a war-footing, or perhaps they show us an organizational structure that was rather separate from real life.