Fernando Desoto's expedition was the first to explore the area. Memphis is one of the "proposed" sites where he built flatboats to cross the Mississippi river.
""On 8 May, 1541, de Soto's troops reached the Mississippi River.[5]
De Soto had little interest in the river, which in his view was an obstacle to his mission. There has been considerable research into the exact location where de Soto crossed the Mississippi River. A commission appointed by Franklin D. Roosevelt in 1935 determined that Sunflower Landing, Mississippi, was the "most likely" crossing place. De Soto and his men spent a month building flatboats, and crossed the river at night to avoid the Native Americans who were patrolling the river. De Soto had hostile relations with the native people in this area.[45][46]
In the late 20th century, research suggests other locations may have been the site of de Soto's crossing, including three locations in Mississippi: Commerce, Friars Point, and Walls, as well as Memphis, Tennessee.[47] ""
Wikipedia
However, it is known that the Lasalle expedition was the first to build a permanent outpost in Memphis. This is chronicled in Parkman's work on LaSalle. They set ashore on the 3rd Chickasaw Bluff (Memphis) to hunt for food. One of the party was lost and after searching for him, it was decided the expedition would continue. A small contingent of men were left behind to erect an outpost and continue the search. They were to be picked up on the return voyage. This was around the mid 1680's.