NJACONS raises a hand:
“Why is everyone assuming that birth rate increase has to be tied to marriage and stay at home moms?”
It doesn’t. Historically speaking, maintaining large harems of concubines acquired by conquest also works well. Alternatively, the mass production of cloned children through the use of artificial wombs and techno-creches would also be a means of increasing the birth rate to a sustainable level. Or, one can simply import Muslims; France has managed to keep its birth rate above the European average this way, although it is still sub-replacement levels.
However, marriage and stay-at-home moms is generally considered to be more in line with Western culture and tradition.