How do we know the New Testament was inspired by God?

A:We can never know that the New Testament was inspired by God, although it is widely assumed to have been.

Speaking of differences in the genealogies of Jesus, between Matthew's Gospel and Luke's Gospel, Raymond E. Brown (An Introduction to the New Testament) says that inspiration does not guarantee historicity or reconcilability; otherwise God should have inspired the two evangelists to give us the same record.

Speaking of differences in the four accounts of the empty tomb, Archbishop Peter Carnley wrote: "The presence of discrepancies might be a sign of historicity if we had four clearly independent but slightly different versions of the story, if only for the reason that four witnesses are better than one. But, of course, it is now impossible to argue that what we have in the four gospel accounts of the empty tomb are four contemporaneous but independent accounts of the one event. Modern redactional studies of the traditions account for the discrepancies as literary developments at the hand of later redactors of what was originally one report of the empty tomb...

There is no suggestion that the tomb was discovered by different witnesses on four different occasions, so it is in fact impossible to argue that the discrepancies were introduced by different witnesses of the one event; rather, they can be explained as four different redactions for apologetic and kerygmatic reasons of a single story originating from one source."

Several of the New Testament epistles have been reliably identified as having been written by anonymous authors, but in Paul's name or the names of other apostles. While done with good intentions, this is not suggestive of divine inspiration.

One of the most spiritual books of The Bible is the Book of Revelation, but many of the early Church Fathers opposed its inclusion in the New Testament. It was eventually included because it was signed by 'John' and some religious leaders thought this John could be the apostle John. Its inclusion was not based on a consensus that Revelation was inspired by God.

Answer:

We are clearly told it is here:

2 Timothy 3:16-17New King James Version (NKJV)

16 All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, 17 that the man of God may be complete, thoroughly equipped for every good work.