Bam Syndrome
That’s right, there is a syndrome out there that makes it possible for people to be born without a nose. We did not think that was even a thing, but here it is and it is called bam syndrome. While it is not life-threatening, it can cause a lot of inconvenience to the person who has it.
They may not have tear ducts, so they can never experience crying, which may be a good thing depending on who you ask. On top of that, it can negatively affect their vision or cause pain in their eyes. Plastic surgery can add a nose, but it would just be for the look and not function.