Maybe I need to add some qualifiers because things are never a start/stop in this world. I'm not going to answer this question yet. But there were operations going on before what you may think was the first Lifeguard service.
In December 1942, Pike, Triton, and Finback aided in an air strike off Midway. April 1943 Tarpon provided navigational aid to an air strike off Naru and Tarawa.
May 16 Whale also provided navigational aid to an air strike off Wake.
While all of these boats had the primary duty of providing navigational aid to these air strikes, they had a secondary duty of rescuing any downed pilots. None did, but the idea of lifeguard duty comes from these actions.
Rear Admiral Charles A. Pownall was the commander of the carrier Task Force in these actions. He would later ask someone if it was possible to have submarine stationed off islands that would be attacked by air. Admiral Lockwood would comply..
Now from this maybe you can come up with the first successful lifeguard mission. I love this question.