A cousin of mine I haven't seen in a very long time recently had a baby. I only found out about it because I received a birth announcement from her. We haven't really kept in touch since we were in grade school and she has lived out of state since college. I'm happy that she had a baby but do I have to send a gift? Is it rude to get a birth announcement from someone and not send a baby present?
There is no formal obligation to send a baby gift in response to a birth announcement. Most often new parents just want to share their joy with everyone and anyone they know (there is definitely nothing wrong with spreading some good news when you have it) and are not expecting a present in return.
Now with that in mind, what a kind gesture it would be to reach out to a long-forgotten relative or childhood friend with a tiny token for their tot, to let them know their happiness is your happiness too. Your cousin thought of YOU as special enough to be personally told of her blessing, take the opportunity to reciprocate and let her know that even though distance has made you drift, she still holds a place in your heart!