When a baby is born here to a temporary (i.e. non permanent) resident how do you go about finalizing the immigration formalities associated with the birth in the HKSAR?
#1 First thing is you need to get the birth certificate from HKSAR.
online submition of baby details
https://www.gov.hk/en/residents/immigration/bdmreg/birth/birthreg/onlinesubmissionbirthreg.htm
Make an appointment for birth certificate
https://www.gov.hk/en/residents/immigration/bdmreg/birth/birthreg/bookbirthreg.htm
Note: Make sure that your VISA validity is more than 3 months. if not, wait for our visa gets renewed, then go for birth certificate, then baby will get visa with validity as same as yours.
#2 Take Oath from HKSAR public services
Find your nearest Home Affairs department in below link, and make an appointment by calling to the number
https://www.had.gov.hk/en/public_services/public_enquiry_services/provided.htm
Declaration form print can be taken from this embassy website
https://www.blsindia-hongkong.com/pdf/annexure-h.pdf
Note: Both parents have to attend to take Oath declaration from HAD.
#3 Apply for passport once you get birth certificate and Oath declaration
refer to this website for required documents, these keep on changing time to time
https://www.blsindia-hongkong.com/passport-newborn-babies.php
Note: HKSAR birth certificate is not valid with in India. Embassy will give another birth certificate upon citizen ship registration.