Don't worry! I heard that for new born, around 1 can of milk powder per week (you can save more money if breastfeeding), which is around HK$150 per can. For diapers, I guess $200-300 per week...
For other bb's stuff like bb bed, bb clothings, you could check whether your friends have 2nd handed. If no, I think you might need several thousands at the very beginning to buy the bb's stuff. But this is just one-off, once you buy them, you don't need to spend more money...