Of all the hotly debated topics surrounding the Gospels and the rest of the 27 ancient writings that make up what we call the New Testament, none is more controversial than the question of WHEN these books were written. The basic line of thinking is this: If the Gospels and the rest of the New Testament books were written while the eyewitnesses of Jesus' life were still around, they are more likely to accurately recount the things that Jesus said and did during His ministry. If they were written decades later, when most (if not all) of the original disciples were dead, then they could easily contain exaggeration, hearsay, and outright falsehood. Therefore scholars who believe the New Testament to be true in its claims about Jesus tend to date the New Testament writings earlier in the First Century, while those who are dismissive of its claims tend to date the Gospels and Epistles much later.
So how big a timeframe are we talking about? Nearly all scholars, skeptics and believers alike, will say the bulk of the New Testament was written in the First Century AD. It's impossible to date most of its books any later, because so many second generation Christian writers - the group collectively called the Apostolic Fathers - quote the New Testament in their own writings, especially the Gospels and letters of Paul. You can't quote something that isn't written yet! As best we can determine, Jesus was crucified in 33 AD, give or take a year or two. None of the Gospels were written while He was alive on earth, and since His teachings were probably transmitted orally for some time, at least a decade or two would have passed before the surviving disciples saw the need to begin writing down His words and deeds. Conservative scholars will say that the Synoptic Gospels (Matthew, Mark, and Luke) were written in the late 50's to early 60's AD, while the more skeptical group will contend that they were written in the 80's or 90's AD. (Oddly enough, both groups agree that the Gospel of John was written last of all, in the mid-90's. There is strong evidence from the Apostolic Fathers and early church history that John lived to be a very old man and wrote his Gospel in the last decade of his long life.)
I would like to point out that, by the standards of ancient history, that is actually a very brief span of time between the events and the earliest written record. For example, our two principal biographies of Julius Caesar, those authored by Plutarch and Suetonius, postdate his life by over a century, yet no one has contended that they are riddled with mythology and inaccuracies! The oldest surviving biography of Alexander the Great was written over two centuries after his death in Babylon. Still, if Matthew, Mark, and Luke were not composed until more than fifty years after the crucifixion of Jesus, then it is more plausible to say that they embellished His life and deeds than if they were written, say, twenty years later, when eyewitnesses both friendly and hostile would have still been around to contradict any false claims.
So where does the evidence point? That is where the Temple comes in. Herod's Temple was a massive structure that utterly dominated the skyline of first century Jerusalem - a massive, imposing edifice of gleaming marble and gold-plated doors visible for miles around. Herod the Great had begun work on it shortly after the Roman Senate named him "King of the Jews" in 31 BC. He did not level the existing temple, built in the 6th century BC by Nehemiah; he simply enlarged it and added onto it until that humble structure was swallowed up by the massive monument to Herod's faux piety. (Herod was not a full blooded Jew and was not related at all to the royal line of King David, so he made an exaggerated show of loyalty to the Jewish religion hoping to make himself more beloved by his subjects. It didn't work - he was a paranoid tyrant and the Jews hated him!)
The Temple was not finished when Herod died around 1 BC, and in fact it was still under construction when Jesus' earthly ministry was going on. It formed the backdrop of many of Jesus' sermons and debates with the Pharisees and Sadducees, and was the subject of one of his most explicit prophecies. During the Passion Week, the disciples commented on the fine workmanship and massive stone blocks that made up the Temple, Jesus said to them: "I tell you, not one stone will be left upon another that will not be torn down!" (Matthew 24:2) No one could believe that such a massive building could be so completely destroyed, and Jesus' criticisms of the Temple were cited against Him at His trial.
But three and a half decades later, in 70 AD, the unthinkable happened. The Romans, sick to death of one Jewish revolt after another, descended on Judea with a massive army and laid siege to Jerusalem. After a year of assaults and counterattacks, they breached the city walls and sacked and burned the entire city. The great temple of Herod went up in flames, and according to Josephus, who was there at the time, the gold plating of the doors and the Temple's mighty dome melted and ran into the cracks between the stones. So after the fires were extinguished, the Roman army, determined to leave no plunder unclaimed, pried up the massive foundation stones and scraped the gold off of them, then tumbled them down to the foot of the Temple Mount where they can still be seen today (I've seen them!).
So here is my point, and I apologize for the roundabout route I took to get here: the Roman destruction of the Temple was a direct fulfillment of the prophecies Jesus Himself made. If the Gospels were written after the Temple was destroyed, WHY DID NONE OF THE GOSPEL WRITERS MENTION THEM?? Here was a prime example to point out the judgment of God on the people who crucified Jesus, to say: "and thus the prophecy spoken by Our Lord was fulfilled." But not a single book of the New Testament mentions the siege of Jerusalem and the burning of the Temple. Not the Gospels, nor the book of Acts (whose story ends abruptly in 62 AD, with Paul awaiting trial in Rome). Paul's letters, which constantly assert the superiority of the New Covenant to the Old, are silent on this topic - but what better way to drive their point home than to point out that the destruction of the Temple meant there was no more need for sacrificial lambs? The anonymous Book of Hebrews, whose entire subject is the superiority of the priesthood of Christ to that of the Levitical priests, never once uses the destruction of the Temple to point out that the old priesthood has passed away.
WHY did the writers of the New Testament pass up such a golden opportunity to point out the accuracy of Jesus' prophecy, and the superiority of the New Covenant? Defensive skeptics have woven all sorts of literary formulae trying to avoid the most obvious conclusion, but applying Occam's Razor, there is only one logical conclusion: the Synoptic Gospels and the Epistles were written BEFORE the Temple fell, before 70 AD. That places them, at the absolute most, 37 years after the crucifixion of Jesus, and quite likely a decade or more earlier. The absence of any reference to the destruction of the Temple in any book of the New Testament is one of the strongest arguments that can be made for the early dating of the New Testament text - and the early dating of the New Testament is one of the strongest arguments for its historical accuracy.