No one seems to have answered this, so I will.
The earliest Christian documents are almost certainly the undisputed letters of Paul, which few find any reason to place later than between 50-60, and with some (eg Galatians) dated possibly in the 40s.
The only reasons for dating any later are claims to pseudo-epigraphy on, say, the pastoral epistles - dates which would be be based simply on when Paul would be well-known enough to imitate. However, note that a significant body of scholarship thinks these letters to be Paul’s.
In the case of the gospels, the tendency even amongst conservative scholars is to take the consensus view for the sake of argument - the reason being that it’s plausible and actually close to events, as historical records go. That consenus tends to place Mark around 60-65, Matthew and Luke/Acts (because they seem to use Mark as a source) maybe late 60s-early70s (some saying as late as the 80s), and John in the 80s-90s.
The older views that the gospels were late and legendary, from the 2nd century or later, are now very much outliers: all seem to have been composed within living memory of the ministry of Jesus.
However, Bishop John Robinson’s book (as linked by Mung) was a refreshing look by a liberal theologian at the suppositions underlying those dates. He found them extraordinarily weak, and came to the conclusion that nothing in any of the gospels demanded a date later than 69AD (the Fall of Jerusalem).
Robisnosn was deliberately provocative, but dated Matthew to 42, Mark to 45, Luke before 56 (with Acts a sequel a few years later) and John to 65 in its complete form. Other scholars, such as John Wenham (who must be OK because I knew his brother!), have also argued for similar early dating overall, and leading NT scholars doing more detailed work have made strong cases for eye-witness testimony even in John (eg Richard Bauckham, (who must be equally good because he lent me his typewriter at uni!). Bauckham employs fascinating evidence such as the frequency of first names in the gospels, which matches the pattern of graves dating to Jesus’s time, but not of those later - much as in England, “George” or “Millie” are now common, but were disliked in my generation.
The reasons for later dating (the weakness of which surprised Robinson, a non-NT specialist) are interesting, and often circular. For example, one key date is the Fall of Jerusalem, prophesied by Jesus in all four gospels. Since future prophecy “doesn’t happen”, Jesus and the evangelsists could not have known the details, and therefore the gospels were written after that date.
However, supernatural insight aside, closer examination shows that in all the synoptics, the apparent details match the Old Testament parallels used by Jesus (eg Daniel) and not the actual seige described by Josephus.
In fact, it’s remarkable that such a cataclysmic event (equivalent even in numerical terms to the Holocaust), cited in the gospels as a vindication of Jesus’s Messiahship, does not have a single mention in any of the New Testment books apart from, in the future, in the gospels. Even in Revelation it is only hinted as imminent. That would indicate a complete NT corpus before 69-70AD.
Other, circular, arguments are based on the assumption that, since the gospels are legendary, they must be late in order for the legends to arise. However, comparison with other ancient legends suggest they’d need to be written two or three centuries after the events for such legends to arise, and nobody even attempts to claim that with the earliest bit of gospel manuscript, from maybe 120AD, being found in Egypt.