Before I start I just want to say that 'm not trying to convert anybody; I just want to point out that Ii's not true that there's no way to prove the Bible is true.
First Of all I would like offer evidence that the Pentateuch was written all at once c. 1200 BCE, instead of the whole Jewish Bible being written around 500 BCE.
Imagine for a second you're a Jew living in Babylon/Persia around 500 BCE. Somebody comes out with a new book called the Bible.; It claims to have been written in parts for the past 700 years. A part of it claims to have been written around 1200 BCE. (This is directly in the Bible "Moses finished writing the words of this Pentateuch in a scroll to the very end" Deut 31:24)
Would you accept it?
And if he claimed it was lost, wouldn't the fact that the book was lost and rediscovered have been written in the Books of Ezra and Nehemiah, which is the story of the period of Jewish History around 500 BCE?
Now Imagine you're an Israelite living around 1200 BCE. A guy named Moses brings this book that he claims is from God. The Book states that your people were in Egypt, and oppressed. Your Opressesors were punished by God in a plague that only effected the Firstborn, after a pretty public prediction of this plague by this Moses fellow. Then it states that your people crossed a sea which split. Then you saw God revealed in fire and smoke on Mt. Sinai. Now, if that never happened who would accept the book?
Nobody.
And furthermore, who in an agrarian society would accept a book that required you to rest the land for a year, once every seven years, and for two years in a row every 50 years if they weren't sure it was from God. Such customs could have really never have developed among the Israelites unless the were told to do it by God.
That's my proof. Even if you don't accept it you can't say we didn't try to prove it.