Eusocial mammals exist, the
naked mole ratWhere most females never go through puberty and most males just never get to participate in sex.
The population wouldn't be stable throughout history, and would need to be able to recover from plagues/ wars/ famines/ et cetra so they'd need to be able to, on occasion, have much more than replacement levels of children. Something like 4 litters per matriarch.
In normal times 2 liters would be the norm with one or three not being uncommon.
Being sapient they will exercise some control over their birth rates. This is something all cultures do and was probably done by Neanderthals and other almost humans.
The one in 4 males surviving raises questions. Biologically, there would be no reason males to be more fragile than kliba since they have the body plan in their genes; so there would need to be special dangers. One such possibility would be if they were like roosters where the males basically kill each other on sight. Another would be that most males aren't "good enough" due to weakness or insubordination and are castrated/ killed, or exiled.
These explanations are pretty horrible, but pretty much anything where you lose 3/4 of a population will be.
If you want your society to not be terrible, I'd recommend that male puberty only happens occasionally with the following genders:
Matriarchs, studs (fertile males), genetically female kliba, genetically male kliba, girls (juvenile females that could become either matriarchs or kliba), and boys.