Imagine you are writing a book of an alternate reality where this is an actuality.
Oh wow. I'm sure there have been a lot of takes on this one in sci-fi and stuff.
Hypothetically speaking, there has to be some kind of evaluation. Who has a home environment of love and nurture? Will some agency or algorithms score homeowners or renters to determine their suitability for child rearing? What does enforcement look like? Is there an underclass or parallel society of dissidents who do not take part in the scoring system and reproduce freely? What happens to them? We could just take the leap and say there is some brain-washing technology which reprograms these people - or they are summarily executed.
What about the pool of birthing persons or those permitted to reproduce in the society? Obviously there must be some means of enforcement. Implants, routine health screenings, constant surveillance of reproductive capacity would be stringent birth control methods. The child is typically the responsibility of the parents. Though when the state interferes it can take this role through subsidies, welfare, child protective custody, court orders, etc. Maybe the children born in environments without love and nurture would have less rights than those born into an environment of love and nurture. Maybe their social credit score would automatically be deemd to be "at risk" for perpetuating the cycle of dysfunctional births and thus endangering the greater good. Or maybe all births would be mandated to be in state run hospitals and those unborn children of women - or men - of too low a birth score would simply be aborted. Unborn children have no rights in this case; they have lesser rights in the former.
If I were writing this short story or book or whatever I would not go this route; it's too obvious, cliche. I would say this type of monitoring system exists - but only in rumor. There is a strong social shaming in place among men and women to curtail sexuality and births. So, something that is self-enforcing: neighbor reports on neighbor, gossiping wives snitch on each other, children are raised with strong indoctrination and messaging to conform - or else. There is a secret police - but no one ever sees them. There are monsters and ghouls that snatch away children in bad households. And there are demons who punish bad parents and attack depraved teens who think about reproducing willy-nilly. Those parents who think their homes are loving and nurturing come up short in this regard; those who are regarded as bad parents are really truly horrendous. Superstition and fear are the means of birth control. And the enforcement is the mob mentality; the group think of the close-knit community. Because survival is not a guarantee for the unborn child. Membership in this community is a gift from parents; people are aware that there are those who exist off-grid, far away, but they are not like us with our love and nurture of children, and they are not good. Occasionally someone is banished and they never come back. That proves the society is superior. There are dangerous animals and predators between us and them; climate change has made the wilderness harsh(er) and desolate. Every month or so about that time, there is a sensational story in the news cycle of failed parenting and the consequences for the children. Every incentive is to obey and you will be happy. The cycle repeats because society is able to maintain this social system without challenges inside it or from outside it.