With the proper breeding techniques and a ratio of say, ten females to each male, I would guess that they could then work their way back to the present gross national product within say, twenty years.
This is like a rejected version of one of Heinlein’s omni-competent hero fantasies. Humans aren’t fruit flies, with anll individuals interchangeable and ready for life shortly after birth. Even ignoring the dubious math getting to those numbers, think about the skills and equipment. In your scenario, everyone’s so busy taking care of food and childcare that they’re not going to have time to realize that they don’t have teachers for all of the subjects or specialists who can maintain intricate manufacturing lines. The people who work on semiconductors can’t just switch to make pharmaceuticals or engines!
Because the men have almost all killed one another off, leaving mostly those who managed to stay out of the fight? Who is supposed to teach the kids skills to rebuild civilization if who's left are wholly occupied with reproducing? Will you kill the infant boys too?
Regrettably, yes. But it is, you know, a sacrifice required for the future of the human race. I hasten to add that since each man will be required to do prodigious... service along these lines, the women will have to be selected for their sexual characteristics which will have to be of a highly stimulating nature.