Do you think archeologists and/or anthropologists have discovered the first jail ever built, or know who built it?

Maybe. There are two possibilities.

"The earliest records of prisons come from the 1st millennia BC, located on the areas of mighty ancient civilizations of Mesopotamia and Egypt. During those times, prisons were almost always stationed in the underground dungeons where guilty or suspected criminals spent their life either awaiting death sentence, or a command to become slaves (often working as galley slaves)."