Must a Christian disagree with Bernard Williams and say the concept of truth does have a history? The Analytic philosopher Bernard Williams believed that the concept of truth has no history: It is the same everywhere, for every culture and language, has been, and will be. He writes as follows in his book Truth and Truthfulness:

One thing I shall not consider, however, is the history
of the concept of truth, because I do not believe that there is any
such history. The concept of truth itself—that is to say, the quite
basic role that truth plays in relation to language, meaning, and
belief—is not culturally various, but always and everywhere the
same. We could not understand cultural variation itself without tak-
ing that role for granted. There are indeed scholarly books that
describe themselves as histories of the concept of truth, but they
typically describe conceptions, varying over time, of belief-forma-
tion, or of knowledge, or of the metaphysical structure of the world (62).

That is, for a sentence to be true in Ancient Greek means the same thing as what it means for a sentence to be true in contemporary Dutch (and so on).
Now, let us say Christians literally believe God is Truth. But clearly, God-in-the-world, for a Christian, has a history. He has always been the same, but the history of his actions in time is very much a history--he has not acted the same in all places and times. After the life of Christ, men and women could not achieve salvation but through Christ as manifest in the world. Even if the concept of God has not changed, God-in-the-world certainly did.
Question: Must a Christian disagree with Bernard Williams and say the concept of truth does have a history?
God has revealed himself. Progressively.
With each revelation, more can be known and understood.
The philosophical thesis you quote (and this may make the question off-topic on this site) falls down completely when one considers that God can only be known (by humans on earth) through the revelation that God gives of himself.
Until he gives it, at a point of time, that truth is not known and cannot be known.
Otherwise He who is truth cannot be known at all.
Therefore, truth does have a history.
That is to say, the body of truth, as made known by God in his word (and documented in holy writings) is a progressive revelation and has a history of such documentation.
By fully studying that documented revelation, you would then  realise that the statement :

... before the life of Christ, men and women could not achieve salvation through Christ . . .

. . . . is incorrect according to the progressive revelation of Deity recorded in holy scripture.
(You could ask more about that in a further, dedicated, question.)