Need a name/word for a child that you wanted and waited really long for

Everyone knows the word "rainbow baby" and I really love that name/word.

It has such a special meaning.

And I really wish everyone that wants their rainbow baby, can hold him/her very soon!

But I was wondering what name/word is there for a child that has been wanted and has been waited for a long time but hasn't had lost a big brother or sister.

For example: you can't get pregnant but eventually you finally are and after +/- 40 weeks you hold him/her.

Or can we make a word for that?

(sorry if this is offending someone)