I have been on the board of one charity which focused on child sexual abuse, and another which tackled sexual abuse (not specific to children). I'll share some thoughts based on child sexual abuse (CSA) because that's the area I'm familiar with (even though I appreciate that the question is broader).

The TL;DR is that the area has caused a large scale of suffering; it's hard to tackle, but I'm optimistic that there might be tractable options out there.

• Prevalence: I've heard people mention CSA prevalence rates that are disturbingly high (e.g. %age rates in the teens or twenties or even higher). I found this surprising. There seems to be some evidence to support this (e.g. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3518746/ ) however this is not a universally held view (e.g. Radford (L) et al 2011 give a figure of 5%, although even "only" 5% is horrible).
• How bad is it per person: Through some of my other volunteering I have encountered many people whose lives have been made dramatically worse because of their CSA, with sequelae including dramatically lowered self-esteem, deliberate self-harm, suicidal ideation/intent and major depressive disorder. In short, there can be grave life-long consequences. However that's just the people I've encountered; how often do people survive relatively unscathed? (I know such people exist)
• Tractability: Some factors will make it difficult to tackle this topic, including the fact that over 90% of sexually abused children were abused by someone they knew (again from Radford (L) et al 2011); this introduces complex family/social dynamics. Furthermore, it's hard to identify those at elevated risk of perpetrating CSA. Past behaviour is hard to use a predictor because it's disturbingly easy to perpetrate CSA and get away with it. Also, anywhere from one-fifth to two-thirds of sexual abuse is committed by other children and young people (source: Hackett, S (2014)). Educating potential victims (i.e. everyone) may be more fruitful, but I haven't looked into this.
• Neglectedness: The ratio of (annual spend on issue by larger charities) / (number of sufferers of issue) seems to be middling for child abuse (not specific to CSA); i.e. probably higher spend (i.e. less neglected) than international aid but less spend (more neglected) than more popular causes such as homelessness and veterans. Note that this is a very rough-and-ready calc

Happy to support/ be involved if anyone wants to look into this further

Copenhagen Consensus is usually the first place I look for things like this. https://www.copenhagenconsensus.com/post-2015-consensus/conflictandviolence

They cite some interventions (reduction of infanticide in UK, reduction of "severe physical violence as a method of child discipline" in US) but the notes are "unlikely that developing countries have the capacity to rollout early child discipline intervention programmes" and "difficult to generalize to low and middle income countries."

Poverty is correlated with child abuse, I would guess mostly because of parental stress.

I looked at the evidence on preventing child sexual abuse (in developed countries) a while ago: https://thewholesky.wordpress.com/2015/10/08/preventing-child-sexual-abuse/ Children are safer from sexual abuse if they live with both parents, if their parents do not have substance abuse, and if their mother does not have mental illness.

So my not very informed guess is that anti-poverty interventions, maternal health interventions (to reduce maternal mortality), and pro-mental-health interventions are likely a good way to go here.

I don't know much about it, but I did skim through the National Incidence Study on Childhood Abuse and Neglect. The thing that stood out to me the most was the massive difference in abuse rates between different family structures:

• Married biological parents: < 3 per 1000
• Single parent with partner: > 55 per 1000

Obviously we can't say this is all causal - in general all good properties are correlated, so it's likely there are shared genetic etc. causes.

I think this is done by 1) reducing parental stress and improving mental health so that abuse doesn't happen 2) reducing dependence of child on parents so they can leave if abuse happens 3) reducing material dependence of parents on each other (women's dependence on spouses is widespread) so either can leave if abuse happens and take their child with them. All three of which are accomplished via poverty reduction, imo. It could inform the ways we go about poverty reduction, such as who is considered "head of household" when distributing money, etc. Access to and education about contraception may also be a plausible way to improve the proportion of abused children. I think another potentially promising and more direct avenue is reducing child marriage. (unresearched opinion)

I see some people suggesting "keep nuclear families together" because of correlations. Since 25% of American divorces cite violent domestic abuse, and that common sense suggests the relative proportion of abuse is higher where reluctance to divorce is higher due to relatively fewer divorces over smaller matters, attempts to keep families together by discouraging divorce will probably increase the severity of abuse (not to mention potentially reducing the happiness and autonomy of the adults) https://www.wf-lawyers.com/divorce-statistics-and-facts/