Primogeniture didn't really exist among the Romans, Celts, or Germanic peoples, or at least was not the only way of dividing property after death. And even in the early versions of primogeniture, other factors like proximity of blood were taken into account instead of absolute primogeniture, allowing women to inherit or people to inherit through women.
All those cultures used primogeniture. Adoption took place too, mostly where there was no male heir, but the eldest son inherited the family estate.
It might be that leadership of a tribe wasn't inherited but that's different to personal possessions. The Celts of the middle ages had a system called tanistry where an heir (tanist) was appointed while the leader was still alive. This could be his son but could also be a male of the same bloodline like a nephew or cousin.