As I have answered it in another mama's post. So, I will only cut and paste my answer here! Hope you won't mind.
"It is difficult to answer, cus both my husband and I are Canadian citizen, who lived in Canada. Therefore, I really don't know the time diffience require for non-residence/citizen applied for his/her child's birth cert.
Based on my experience, we applied the birth cert online, and received it in about 2 weeks.
The passport office said it will take 2 weeks to receive my baby's passport, but we get it in about 1 week. However, the passport application does require a birth cert number to prove of citizenship!"
Please apply your baby's birth cert asap, so you can get his/her passport application going!