The "First Crossing" referred to the 15-year, one-way journey that the original Pern colonists made from Earth to Pern. Most of the colonists were in suspended animation for the entire 15-year trip. The crew of the colony ships were awake for 5-year shifts, and asleep the other ten.
The dolphins called this the Great Sleep. The "Name Song" remembered the names of the 25 dolphins who made this crossing aboard the Bahrain.