Your question assumes there is no WILL in a person, but only pure REASON and that what should convince will in all cases convince. But that is surely not the case :)
As far as Judaism and Christianity go, the conviction (Faith) preceded the books.
Also, you make that false distinction, either written by God or written by men but the Bible takes that as wrong.
Jesus convinced His followers that He was the Son of God so that automatically validates the OT. And since it is simple history that He set up a Church , that Church validates what is and is not a teaching of Jesus.
But the WILL is the primary in all this, not reason. The person you are thinking of would be actively searching for what his reason could tell him and would be of good will when a revelation came. Unless God is good, anybody could be fooled.