Paul also accepted Luke's writing as Scripture...
Yes, I know.
For any who might not know what we're referring to, we're referring to this:
I Timothy chapter 5
[
17] Let the elders that rule well be counted worthy of double honour, especially they who labour in the word and doctrine.
[
18]
For the scripture saith, Thou shalt not muzzle the ox that treadeth out the corn.
And, The labourer is worthy of his reward.
Here, Paul cited two scriptures. The first is found in Deuteronomy 25:4, and the second is an exact quote of a portion of Luke 10:7 in the underlying Greek.
"And in the same house remain, eating and drinking such things as they give:
for the labourer is worthy of his hire. Go not from house to house." (Luke 10:7)
It is generally believed that Paul wrote his first epistle to Timothy somewhere around 65 A.D., so this means that the gospel of Luke would have already been in circulation at that time. Luke was a travelling companion of Paul, but don't let anybody deceive you into believing that Paul merely received this via word of mouth from Luke. No, Paul used the word "scripture", which is "graphē" in the underlying Greek, and this word means "a writing or a thing written".
Paul used these same introductory words of "for the scripture saith" in Romans 9:17 in relation to what had been written by Moses in the book of Exodus, and again in Romans 10:11 in relation to what had been written by the prophet Joel in the book of Joel.
Surely if we can define Scripture as the revelation of God's plan for humanity,
which is what it is, it makes me wonder if they knew they were writing Scripture
at the time, especially in regards to the gospel writers. Paul may be surprised,
after all, to discover how much his letters came to be accepted as such 
Well, Luke, for example, certainly seemed to know exactly what he was doing when he penned his gospel.
We read:
Luke chapter 1
[
1] Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us,
[
2] Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word;
[
3] It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus,
[
4] That thou mightest know the certainty of those things, wherein thou hast been instructed.
There's a difference of opinion in relation to whom Luke was actually writing. Some believe that Luke was writing to an individual named Theophilus. Personally, I disagree. The name Theophilus literally means "lover of God", and I believe that Luke had a general audience in mind while writing which consisted of all lovers of God. In either case, we need to notice that Luke said that "MANY have taken in hand to set forth in order a declaration of those things which are most surely believed among us, even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word".
Well, who are these "many" who were eyewitnesses from the beginning and ministers of the word?
It seems to me that he was talking about certain apostles whose writings preceded his own, so it's quite possible/probable that Matthew's gospel, at least, preceded Luke's gospel. It's also generally believed that Mark got his gospel from Peter, so Mark's gospel may have preceded Luke's gospel as well.
We do have at least one indication from Paul's epistles that either Matthew's or Mark's gospels (or both) were already in circulation during his day as well.
I'm referring to the following:
"And though I have the gift of prophecy, and understand all mysteries, and all knowledge;
and though I have all faith, so that I could remove mountains, and have not charity, I am nothing." (I Corinthians 13:2)
How did Paul know about faith that could remove mountains?
Did he learn of the same by reading either Matthew's or Mark's (or both) gospel accounts?
"Jesus answered and said unto them, Verily I say unto you,
If ye have faith, and doubt not, ye shall not only do this which is done to the fig tree, but also if
ye shall say unto this mountain, Be thou removed, and be thou cast into the sea; it shall be done. " (Matthew 21:21)
"For verily I say unto you, That whosoever shall say unto this mountain, Be thou removed, and be thou cast into the sea; and shall not doubt in his heart, but shall believe that those things which he saith shall come to pass; he shall have whatsoever he saith." (Mark 11:23)
It's quite possible that he did.
Here's something else which indicates early authorship of the gospels:
"The former treatise have I made, O Theophilus, of all that Jesus began both to do and teach," (Acts 1:1)
Luke authored the book of Acts, and when he spoke of "the former treatise", he was referring to the gospel of Luke.
Well, the book of Acts follows the exploits of Paul, and it ends with Paul yet being alive. Although we don't know the exact date of Paul's death, it's generally believed that he died somewhere between the years of 65 A.D. and 68 A.D. at the latest. Luke recorded James' death in the book of Acts, so it would be very odd for him not to record Paul's death if Paul was indeed dead at the time of his writing. Furthermore, the temple in Jerusalem is still standing in the book of Acts, and that was destroyed in 70 A.D., so it's basically certain that the book of Acts was written sometime before 70 A.D. Again, seeing how Luke's gospel PRECEDED his writing of the book of Acts in that it was his "former treatise" (Acts 1:1), we know that his gospel was written even earlier than this.
Anyhow, just some internal witnesses from the Bible in relation not only to their writings being counted as scripture early on, but also regarding the timeframes surrounding said writings.
