It can take forever but if you are in a shelter like Chasity said you can update your account saying you are homeless and your priority will priority be raised and you'll get it faster atleast you'll get I to nycha faster vs section 8.
I feel like if they opened it for a set time period then it really shouldn't be a long wait but I guess just pray about it and be patient.
It can take months or years.. If you’re in the shelter, you can ask for a NYCHA referral to make the process quicker.. Good luck with everything!