Good morning.
I'd like to begin by sharing a complaint with you. A constituent informed me that his SIN card was mailed to him in an unsealed envelope. I find that rather odd. If you do use envelopes, you should check to be sure that they are properly sealed.
You mentioned that Service Canada works quickly to issue SIN card. I hope you're not just acting quickly for statistical purposes, so that Service Canada can claim to be doing its job well, because the potential for errors exists. I think this is a very important point.
When they were born, I applied for SIN numbers for my daughters. I didn't have any problems. However, waiting one, two or three months doesn't make much of a difference to a three-month-old baby. He's not about to use the SIN to get a job at McDonald's. Therefore, I think you need to proceed very carefully when you issue a SIN to a newborn.