When my mother went into labor with me prematurely, she was afraid that I might not survive. So, while she was in delivery, the priest was waiting outside to baptize me immediately. However, doctors said I was tiny (5.4 lbs) but would survive, so the priest simply said a prayer over me and blessed me.
However, since I was so small, my family were hesitant to wait the 40 days....just in case the doctors were wrong, and therefore, baptized me on day 3 of life.
It was in the midst of a snow storm, so the priest very graciously came out to our house to perform the sacrament.
So I, for one, didn't have to wait the 40 days!