Question: "Is there proof for the inspiration of the Bible?"
Here are some evidences that the Bible is inspired (God-breathed) by God, as declared in 2 Timothy 3:16.
1) Fulfilled prophecy. God spoke to men telling them of things He would bring about in the future. Some of them have already occurred. Others have not. For example, there were more than 300 prophecies concerning Jesus Christ's first coming 2,000 years ago. There is no doubt that these are prophecies from God because of manuscripts and scrolls dated before the birth of Christ. These were not written after the fact. They were written beforehand. Scientific dating proves this.
2) The unity of Scripture. The Bible was written by approximately 40 human authors over a period of approximately 1,600 years. These men were quite diverse. Moses, a political leader; Joshua, a military leader; David, a shepherd; Solomon, a king; Amos, a herdsman and fruit picker; Daniel, a prime minister; Matthew, a tax collector; Luke, a medical doctor; Paul, a rabbi; and Peter, a fisherman; among others. The Bible was also written under a variety of circumstances. It was written on 3 different continents, Europe, Asia, and Africa. Yet, the great themes of Scripture are maintained in all the writings. The Bible does not contradict itself. There is no way, apart from God the Holy Spirit supervising the writing of the Bible, that this could have been accomplished.
Contrast this with the Islamic Koran. It was compiled by one individual, Zaid bin Thabit, under the guidance of Mohammed's father-in-law, Abu-Bekr. Then in A.D. 650, a group of Arab scholars produced a unified version and destroyed all variant copies to preserve the unity of the Koran. The Bible was unified from the time of its writing. The Koran had to be unified through the editing of men.
3) The Bible presents its heroes truthfully with all of their faults and weaknesses. It does not glorify men as other religions do about their heroes. When you read the Bible, you realize that the people it describes have problems and do wrong just as we do. What made them great was that they trusted in God. One example is David. David is described as “a man after God's own heart” (1 Samuel 13:14). Yet, David committed adultery (2 Samuel 11:1-5) and murder (2 Samuel 11:14-26). This could have been left out of Scripture to hide these details of David's life. But God included these things.
4) Archaeological findings support the history recorded in Scripture. Though many unbelieving people throughout history have tried to find archaeological evidence to disprove what is recorded in the Bible, they have failed. It is easy to say that Scripture is untrue. Proving it to be untrue is a different story. It has not been done. In fact, in the past the Bible contradicted the current “scientific” theories, only to be proven later to be in fact true. A good example is Isaiah 40:22, which declared that God “sits on the circle of the earth” long before scientists claimed the earth was flat.
The Bible’s claims of being from God should not be understood as arguing in a circle or by circular reasoning. The testimony of reliable witnesses - particularly of Jesus, but also of others such as Moses, Joshua, David, Daniel, and Nehemiah in the Old Testament, and John and Paul in the New Testament - affirm the authority and verbal inspiration of the Holy Scriptures. Consider the following passages: Exodus 14:1; 20:1; Leviticus 4:1; Numbers 4:1; Deuteronomy 4:2; 32:48; Isaiah 1:10, 24; Jeremiah 1:11; Jeremiah 11:1–3; Ezekiel 1:3; 1 Corinthians 14:37; 1 Thessalonians 2:13; 2 Peter 1:16–21; 1 John 4:6.
Also of interest are the writings of Josephus, an historian who recorded much of the history of Israel during the first century. In this he records some events which coincide with Scripture. Beware though, his writings are rather lengthy. Considering the evidence given, we have no choice but to accept the Bible as being from God (2 Timothy 3:16).