Each observation gives a terminus post quem or a terminus ante quem for the wall. Sort them.

TPQ (wall is no earlier than…): A 350 CE coin sealed in the wall’s foundation trench, Pottery of the 4th century mixed into the wall’s mortar, A timber felled in 380 CE reused in the wall’s base

TAQ (wall is no later than…): The wall is buried beneath a datable 600 CE destruction layer, A 550 CE grave is cut down through the wall’s ruins, A 500 CE floor runs over the wall’s demolished stub

Everything inside or beneath the wall pushes its date later (TPQ); everything sealing or cutting its ruins pulls the ceiling earlier (TAQ). Between the two termini lives the wall.