In an absolute sense, it cannot be proven. Nor, for that matter, can I prove that you exist and vice-versa. But in the real world we all make assumptions based on strong probabilities.
In the case of the Bible, we're talking about the most influential -- and most criticized -- book ever written, and it's stood up to challenge after challenge.
In addition, it's remarkable as a historical record. Most of the sacred writings of the other great religions are merely collections of sayings or advice, etc. Therefore, it's sensible to trust the Bible in what it says, and in what it says of itself. Of course, that doesn't mean that if any individual chooses otherwise, that such isn't his right.