That's certainly not what most historians would say. Wikipedia has an article on dating the Bible and 70CE is the earliest date for Mark, with Matthew and Luke later than that. John is listed as possibly as late as 110CE.
Mark alludes to the war that began in 64CE, that eventually led to the destruction of the temple in 70CE, but does not mention that destruction. Thus, for the majority of scholars, Mark must have been written before that moment.
Further, Burkett and Duling date Matthew to within a decade of Mark being written, because of similar events that should have influenced the writing if it was later, but did not. On the other hand, some suggest an even earlier date to 40-50CE (Wright, Wenham).
You won't be able to force the synoptics to a "much later date", as they were dated and discussed (poorly) by Papias of Hierapolis in 95-110CE. Therefore the works happened before this. As he was also "a hearer of John", you also can't date the Gospel of John after Papias was already dead.
The majority view is that the synoptics were written within living memory of the original witnesses, as I've already stated.
But late dating creates a host of disparate problems that must be explained. One problem coming to mind: Acts of the Apostles clearly ends with Paul still being alive.
If you simply don't share the assumption that prophecy is fundamentally impossible, then early dating for Mt, Mc and Lc becomes easy to accept on the basis of evidence.