I know this by faith. But evidence does corroborate the Bible.
Here's one of my favorite arguments in favor of the Old Testament's inspiration:
1) In Genesis there are passages that state alternately that "God created man in his own image (Gen 1:26)" and ""Let us make man in our image (Gen 1:26)." (This apparent contradiction is easily reconciled with the doctrine of the Trinity)
2) The Jews were nothing if they were not monotheists. This passage clearly seems to contradict monotheism.
3) The Jewish scribes had centuries within which to edit the manuscripts containing these passages, yet one can only conclude that they did not do so.
4) We can thus conclude that the scribes were scrupulous in the re-copying of Scripture.
5) God said to Moses, "I am who I am" (Exodus 3:14) or "I AM."
6) God's name represents a metaphysical insight into the nature of God that was not fully developed until the mid 1300's with Thomas Aquinas. That is, that God's essence and act of existence are the same.
7) It is extraordinarily unlikely that Moses was a philosophical genius 2000 years ahead of his time and also a liar, putting his words into the mouth of God.
8) Since we can know by natural reason that there are truths superior and unknowable to unaided natural reason, and that God can reveal super-reasonable truths about Himself to us, it is logically possible that God revealed His name to Moses.
9) Considering#7 & #8, it is far more likely than not that God revealed His name to Moses.
10) In consideration of #4, we can be reasonably certain that the account of the theophany of the burning bush is accurately recounted in Scripture.
11) Therefore we can be reasonably certain that God really did have a special relationship with the Jewish people since Scripture attests that Moses occupied a prominent place in Jewish society and a prominent role in Jewish history.
12) We can therefore be reasonably certain that the oral and written Traditions handed down to us from the Jews as inspired really are inspired.