I have several thoughts...
First, I understand why many have focused on the issue of him being spanked with a belt, but honestly I am just as concerned/saddened by the idea that someone was methodically going to the garbage and throwing away all his toys! Yes, a 9 yr old could have done something awful, but my gut from what little you've heard so far is that this is a longstanding pattern in this home.
It's just a gut, please, no one mistake me for saying she should act on my little opinion on that!
Here's my advice though, given my gut: definitely take the PPs advice and ring the doorbell, comment that you're both moms (does anyone else live there with the mom and boy?), and that you'd love to have her over for coffee.
If she says yes, great, see if you can build a relationship and definitely make sure she brings her son over, even if your kids are not the same age. Ask her what her son likes and try to show that you are interested in his interests. If you can and are up to volunteering to babysit, YES yes yes, please do that.
Another thing to please do - although I know in NYC it's possible to live across the hall from soemone and rarely see them - but *whenever* you see her son, go out ofyour way to be nice to him. Anything you can say that's nice and positive, say it. He needs to hear it - of that, I am sure.
If she isn't interested in coffee or she says yes but never follows through, then next time you hear something going badly, go ahead and knock on the door (if you're comfortable with this) and simply say "Hi, just checking in, wanted to make sure you're ok and see if I can help with anything". Yes, that might annoy them if they were in the middle of a big issue, but it interrupts the mania, gives everyone a second to breathe, and also gives you a chance to see if you see/hear anything that raises your concerns so much you feel you need to call CPS. But it ALSO gives you a chance to offer specific help, if mom feels like telling you what is going on, maybe you can say "Oh, I can see how that can feel like a really big deal, but maybe you can manage it this way..." [hopefully you get what I'm trying to say - hard to offer specific words of support not knowing what you might see/hear].
I have been and always will be a big believer in not standing by if you hear a big amount of tension in a home that affects a child and trying to offer whatever little bits of support/positivity/relief you can manage. And if a child is really in danger, i.e. if you hear him screaming again, go ahead in the hall (if you can and feel able to) and listen more to see if you feel like you need to call CPS.
I do understand that people have different levels of comfort/discomfort with intervening when they worry about someone else's child, but there is *always* *something* that you can do, however big or small, that may make a difference for that child. Find that something... it can make a huge difference.