According to the in-game description of Subject Delta, previously with the nickname of "Johnny Topside", he was originally a member of a deep sea diving expedition that discovered the underwater city of Rapture, though it is not stated whether they stumbled across the city by accident or were looking for it specifically. After being captured by Andrew Ryan's forces, it was decided that the divers couldn't be let go, lest they share the secret of Rapture with the surface world, and so the men were "volunteered" to become the Alpha Series, the prototypes of the Protectors who would eventually be called "Big Daddies".
The Alpha series aren't quite as well armored as the later Big Daddy models, such as the Bouncer or the Rosie, but they were capable of using Plasmids, and had the ability to wield multiple weapons instead of just having one. One of the biggest differences between them, though, is that each of the Alpha Series subjects were pair-bonded to a specific Little Sister, whom they would think of as their daughter, and who would think of them as her father. Subject Delta was bonded to Eleanor Lamb, daughter of Sofia Lamb, who eventually laid a trap for Delta, catching him off-guard with a Hypnotize Big Daddy plasmid, and forcing him to shoot himself in the head so she could reclaim her daughter. However, he somehow survived the gunshot wound and mysteriously woke up ten years later, eight years after the events of BioShock. An "incentive" built into the early Big Daddies to make them want to protect their charges now threatens Delta's life: if he is separated from Eleanor for too long, he will slip into a coma. Upon waking up in Lamb's Rapture, he sets off to reunite with Eleanor, both to preserve his own life and to save her from her mother.