Not directly. Jews did not build monuments to themselves.
What we know is there are two inscriptions speaking of
"the house of David." Meaning a dynasty, which is usually
named after the first King.
But many who claimed "there is no evidence of King David"
don't openly say now, "I was wrong." They move onto some
thing else. This is one reason why I am impressed by the
bible - the intellectual dishonesty of many of its enemies.
Alledgedly speaking of the house of david, there is considerable controversy on the understanding and translation.
Many who say there is evidence seem to skip the doubt