The first Elf to awaken in Middle-earth was Imin. He awoke at Cuiviénen alongside his wife, Iminyë, before the Sun and Moon existed and while Middle-earth was lit only by starlight.
Imin was the first of three Elf leaders named according to order. After awakening, he and Iminyë encountered other newly awakened pairs. Tata and Tatië were the second pair, while Enel and Enelyë were the third. These early Elves became the ancestors of the major Elven kindreds and communities that later shaped the history of Middle-earth.
The name Imin itself means “First,” making the answer a deliberate piece of Tolkien’s naming system. He should not be confused with Ingwë, who later became the leader of the Vanyar and High King of the Elves, or with Elwë and Finwë, who were prominent rulers of other Elven peoples in later ages.
The awakening took place during the Years of the Trees. The Vala Oromë eventually discovered the Elves and brought news of them to Valinor, beginning the chain of events that led many Elves to undertake the Great Journey westward.