REMEMBER EILEITHYIA? - I DID NOT
Leto - Apollo - Artemis (Diana)
Labour, Delivery, and Birth - Midwife
Eileithyia was the daughter of Zeus, but not by his wife Hera. She may have had roots in Laconia in Elysia (the future lands of Sparta) and the root of her name. Her task was to prevent Leto from giving birth to Apollo and his twin sister Artemis. Thereafter, she became the emblem and a Greek goddess of childbirth.
Eileithyia is arguably one of the most ancient known pre-Hellenic goddesses. The fact that most and I, and, probably, you do not know of her, indicates that regardless, we celebrate birthdays. In short, every birthday celebration is in memory of Eileithyia and the birth of her twins, Apollo and Artemis (Diana).
For the story of Leto seeking a safe spot (eventually in the island of Delos) to deliver her twins and the failure of Eileithyia to fulfil the command by Hera to prevent the delivery, implies to me two notions - only mortals are "born" - deities materialize. For more, please explore the links above.