We just moved from NYC in June. My 2 kids attended p.s. 40. We got our lists on the 1st day of school and had about a week- 10 days to bring in the supplies. The only thing hard to find after school started for me was the kindermat for nap time. K-mart has them for about $5. This past year, our school store was actually selling them. Also, for what it's worth, school supply lists are suggested donations, so I wouldn't stress yourself over some of the items if you can't find them! We usually found most of our supplies at Office Depot(union square) and K-Mart(Astor Place).
Congratulations on the new baby!

unfortunately that is pretty normal, my daughters old school only gave out the school list when they finshed one grade and moved up to the next so when she graduated from 1st grade and got her final report card in june there was usually a standard list of what she would need to 2nd grade, but as a new student they usually do not provide any list for parents who end up scrambling around on the first day of school along with the other parents trying to find the supplies that are needed.