OP, on the bright side, the Ferber cry it out method is a short term thing. After one week, the baby should be crying a lot less. Mine was fine after three days, which is a typical span of time. Not to say she doesn't cry now and again but the hour long scream fests are over. It sucks for you now but it will pass pretty soon. Unless they're doing it wrong and being inconsistent--which can cause the method to take much longer. Chin up, things will progress soon.

The "cry it out" method is a western world way of thinking. There are other ways to take care of babies and they grow up just fine. Remember people, the west is not the centre of the universe. Your way of parenting is not the only way. Also many babies that had to cry it out turn out okay too ;)

I have no idea what kind of parents they are but we had the misfortune that our baby was a "cry baby" who seldom stopped, we went to a "baby cry ambulance" to not go crazy ourselves. Fortunately we have a big house with no direct neighbours but it was like the first seven month were a horror movie.

Ask the parents to cover the floor of the kid's room with industrial safety flooring pads. They are cushioned so the are baby-friendly for falls, and though they're not designed specifically for it, they're thick enough to block baby-crying frequencies of sound fairly well. Maybe offer to split the cost so everyone wins.

Get yourself some earplugs, then play heavy metal at 3am.

The "let them cry it out" method is probably the best way to do it, at least in theory. Coddling the baby shelters it, keeps it from getting over its issue.

You could always..... Kill them......

People, neglecting a child and letting them cry all night and the Ferber CIO method are entirely different. Letting a child cry continuously without checking on them is neglect. Letting them cry after you have checked that they aren't in duress that you can and should abate through intervention is not neglect. If the baby keeps crying for long enough, he's a parent should intervene, but sometimes there is really NOTHING a parent can do. I cried all the time as a baby- and I mean, almost nonstop unless I was being fed, sleeping or bathed- because I was not only lactose intolerant but had acid reflux, in addition to being premature and having jaundice as a result. I know that my mother ran herself ragged trying to soothe me- with an infected cesarean section wound and her body rejecting the sutures- and I also know that I was like that for the entire first six months. There were times that my mother- or whoever was watching me at the time- had no choice but to let me cry myself into sedation. The doctors couldn't do anything, no change is diet helped, all the treatments I was given had side effects that- surprise!- made me cry more. The only person I let hold me was my mother, and even swaddling was a fifty fifty shot on whether it would help. So, please, before you tell someone to report parent(s) to the Child Protective Services, at least ASK if their child is having health issues. Yes, as in, go up to them and ask. Because they are probably embarrassed and upset that they can't soothe their child, and probably just as upset as you are, if not more. If you ask them and they tell you that yes their child has health issue, suggest that they let the other tenants know, and maybe do something to make up for it. If they say that they don't know- as in they haven't taken the child to a doctor over it- suggest it. IF something from the interaction hints that the parent(s) are neglecting or abusing the child or the parent(s) seem to be exhibiting severe signs of Post-Partum Depression that indicate they might be a risk to the child, themself, or others, THEN you call CPS. As to those that are saying that all parents 'choose' to have children, I've got two phrases for you: conception by rape and emotional blackmail. Not all pregnant persons can get to a clinic or pharmacy for contraceptives or abortion. Some will be pressured into keeping the child, usually by religious or family pressure, others by their dating partner via emotional manipulation- a lot of people in those cases also do not have adoption as an option for the same reason. Others may not be in a position that they can even access any sort of pregnancy termination until the period in which abortion is permitted has passed. Laws regarding the allowance of contraceptives and abortion are always at risk of change. Clinics get robbed and attacked because of the services they provide. Both abortions and emergency contraceptives require money, and many insurances won't pay for them. Doing "at home" abortions are not only unsafe for the pregnant person, but is illegal in some locations, or could set the precedent for making them illegal. Or someone may have to take in a relatives infant with no warning due to death or illness. So, yes, people can and in fact do get stuck with children they didn't "choose" to have. More often than people seem to think. Life doesn't always wait for you to be ready before throwing something unpleasant in your face. Assuming that someone has a child because they wanted to have a child ignores a very real subset of people that exist. And since I haven't seen very many people acknowledge this, many "family apartment housing" complexes have rule and protections in place in relation to noise produced by young infants and children. TL;DR: The Ferber method can in fact be both safe and have appreciable effects when done correctly, and instead of jumping to calling child protective services, actually do SOME sort of check to see if it is in fact a matter CPS should be involved in. They've got enough on their plate without having to investigate someone because a neighbor skipped straight to contacting them.

Imagine being 'in the wild'. A screaming baby is a call to predators that there's an unintended infant - you're clearly not *supposed* to leave babies to scream their heads off. I screamed myself to sleep every night as a baby, which may have something to do with why I had major sleeping problems until my late teens. My grandmother was banned from babysitting me after it was discovered that she comforted me in the night when I was screaming so that I settled down. :(

(Someone may have said this already) Is there any way you could politely ask them if anything could be done? EG helping them/you sound proof a bit. Obviously say that you appreciate babies don't work on our clock or by our rules etc. You could take up a cake or something too, so they know you're friendly and just want sleep...