What to do having a baby crying as neighbor ?

You could try ear plugs, or moving your bed to another room if it is affecting your sleep that badly. Heavy blankets on the wall may also help deaden the sound. Or you could see if you could find a louder fan or white noise machine. When my son was an infant and I couldn't stand the crying any more (and he was changed and fed and we'd tried everything else to make sure his needs were met) I would strap him to my chest and run the vacuum to drown out the sound of the crying. By the time I got one or two rooms done, he had usually fallen asleep.

If you choose to try talking to the parents (which I don't really recommend if you do not know them and have never spoken with them before), start with a compliment on their baby, perhaps also a congratulations on the new addition. Then offer condolences that she seems to be a colicky infant and how hard it must be for them to be loosing so much sleep. This will soften any hard feelings from you complaining about the crying which, as you have acknowledged, they can't really help. Then, maybe suggest moving the baby's sleeping arrangements or taking the baby to another part of the apartment when she wakes in the middle of the night as you have also been loosing sleep.

In addition to buying several pairs of ear plugs, you could also consider additional soundproofing of your wall, and, if the noise is also coming from the window, also get some soundproof curtains installed over your window.

Acoustical foam, the kind that people are using in their media rooms, could be an easy solution to reduce your noise. That way, perhaps you would not even need to wear the annoying ear plugs.

get ear plugs. but if the baby literaly cries all the time you mught call child protective services the baby may not be being taken care of properly. if you live in a house than hearing the baby is unusual if its an apartment then not so much.

Ear plugs. Not much else you can do. These things happen when you live close together.