Under a blistering sun, Nicholas M. Luccketti swatted at mosquitoes as he watched his archaeology team at work in a shallow pit on a hillside above the shimmering waters of Albemarle Sound. On a table in the shade, a pile of plastic bags filled with artifacts was growing. Fragments of earthenware and pottery. A mashed metal rivet. A piece of a hand-wrought nail.

They call the spot Site X. Down a dusty road winding through soybean fields, the clearing lies between two cypress swamps teeming with venomous snakes. It is a suitably mysterious name for a location that may shed light on an enigma at the heart of America’s founding: the fate of the “lost colonists” who vanished from a sandy outpost on Roanoke Island, about 60 miles east, in the late 16th century.

On and off for three years, Mr. Luccketti and colleagues with the First Colony Foundation have been excavating parts of the hillside, hoping to find traces of the colonists. As if clues in a latter-day treasure hunt, hidden markings on a 16th-century map led them to the spot on the sound’s western shore, which Mr. Luccketti had previously surveyed.