How I see it....
While many scholars believe that the gospels were finished years after Jesus' death, it doesn't necessarily mean the authors didn't
begin to write them while Jesus was still alive. At the end of John, it says, "It is this disciple who testifies to these things and has written them, and we know that his testimony is true" (John 21:24)
Writing back then was a pain staking process. It's not as if anyone who wanted to write could simply jump on their camel and gallop down to the nearest Office Max and buy a ream of paper and a few quills.
The gospels were written by hand on papyrus. First, you'd have to either find some papyrus at an affordable price or make it yourself. It wasn't always available, nor was it always affordable. And if you wanted to make it yourself (provided you knew how), the process took about a month or longer, AND, you couldn't harvest the plant throughout the year (it died in the winter and the roots rotted).
Add that to some other limitations, such as, having to feed yourself and tend to your 'goats', your family, and being forbidden to do ANY kind of work on the Sabbath...
See where I'm going?
Yes, many scholars agree that the gospels were
probably written years after Jesus' death. But the key word is "probably", and there are some scholars who submit that the gospels were written
partially during Jesus life, and shortly after his death.
The fact that those scholars agree that the books were
probably written several decades after Jesus death does not have me convinced that they
absolutely were.