How do we know the OT came before the NT?

Is there historical evidence that the Old Testament was written before the New Testament? One aetheist claim that I have encountered is that the Old Testament was written at the same time as the New Testament, therefore, the prophesies, oracles, etc., are nothing more than creative writing

The oldest surviving manuscripts found so far date to around the 2nd Century BC. So there is about 200 years between the oldest surviving fragments of Hebrew Scripture and the birth of Jesus.

However, the idea that the Old Testament was written by Christians is absurd. How would one explain Judaism? Why would they adopt as the Word of God the writings of a group that they do not believe?

It also makes no sense that anyone would believe in Jesus as the fulfillment of prophecy if the prophecy did not predate his existence. How could Jesus have convinced people to follow him without appealing to something that already existed?

On top of the common sense, most scholars date the books of the Hebrew Scriptures to be centuries before Jesus.

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