First off
The prevalent view throughout history is that the OT histories, including Genesis 1-11, are genuine history (and, further, that Earth was Created circa 4,000 BC). Moreover, there is much historical and archaeological evidence for much of the OT. Simply on a probabilistic standpoint, it is likely that the NT authors agreed with the majority opinion of the day in accepting the OT as genuine history.
Note also that I don't use the word "literal" in the preceding paragraph, as that term is frequently subject to misuse and abuse. No one believes that there are literal barred gates restraining the ocean (Job 38), but that is a different claim than the historical claim that God caused "the waters under the heavens be gathered together into one place", thus forming dry land (Genesis 1). When we hear that "the voice of [Abel]'s blood is crying to [God] from the ground", and that "the ground [...] has opened its mouth to receive [Abel]'s blood from [Cain's] hand" (Genesis 4:10-11), we recognize that figurative (rather than literal) language is being used, but that the event so described is nonetheless real history.
It's important to note that this is simply the way humans communicate. That dress in the window "screaming 'buy me!'" doesn't have a literal voice, but the temptation to purchase it is nevertheless real. The sun doesn't literally rise or set, but if you ask anyone what time sunrise was/is, they know what you mean. The use of figurative language does not imply that the events so described are necessarily not genuinely historic.
Scriptural Evidence
That said, what evidence can we find from Scripture itself that this view is correct?
For starters, we have the genealogies of Jesus, which go back to "Adam, the son of God". These acknowledge Adam as a special Creation, and no Scriptural genealogy contains any suggestion that the lineage from A to B is mythical while the lineage from B to C is historical. The implication, therefore, is that the entire lineage from A to C — that is, from Adam — is historical.
We have Peter's writing; "the earth was formed out of water and through water by the word of God, and that by means of these the world that then existed was deluged with water and perished" (2 Peter 3:5-6). There is no indication Peter is speaking of a mere myth; in fact, not only does he explicitly describe Noah's Flood as a "fact", but specifically predicts that scoffers will come who deny this fact. The combination of such an explicit description and a prediction of future denial of the same ought to give serious pause to anyone doing such denying.
Peter also mentions Noah and the Flood in a way that strongly implies historicity in 2 Peter 2:5, followed immediately (v6) by mention of Sodom and Gomorrah. Sodom (see below) is affirmed as factual by Christ Himself.
Paul repeatedly mentions Adam, Eve and the Fall with no indication he is speaking of myths. The most straight-forward reading of these citations would be that Paul believed them to be genuinely historical. The context is also important; Paul uses Genesis 1-3 as the basis for many theological teachings, which would be seriously undermined if he was referring to myths rather than true history. (Indeed, the entirety of Christian theology significantly relies on the historicity of Genesis 1-3.)
Moreover, Paul states that "[God's] invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world" (Romans 1:20). What, exactly, is around at the beginning of Creation to do such perceiving, if not Adam and Eve? In the same passage he warns of "men, who by their unrighteousness suppress the truth".
We have Christ Himself; when he refers to Adam and Eve, he uses the formula "have you not heard/read?". As best we can tell, this formula is used in various places to affirm the truth of the Scripture being quoted. In the same context, Christ tells us that "at the beginning of creation God 'made them male and female'".
In Matthew 11:20-24, Jesus mentions judgment for Tye, Sidon and Sodom; how will their judgment be more bearable if these places never existed? How could Sodom "have remained until this day" if it never existed? The clear implication is that these were real places.
Again, in Luke 11:50–51, Jesus mentions Abel as a prophet alongside Zechariah. Certainly some of the prophets were real, which would make Abel's inclusion rather odd if Abel were not also real.
Again, in John 5:46-47, Jesus says "if you believed Moses, you would believe me", and offers this challenge: "if you do not believe [Moses'] writings, how will you believe my words?"
Lastly, we have the direct Word of God Himself, when he says "in six days [I] the Lord made the heavens and the earth".
What's missing, despite heroic efforts by some people to insert such, is any evidence that the authors of Scripture (OT or NT) believed the histories therein to be other than genuine.
Aside
Of course, whether or not the NT authors believed the OT to be historically accurate, we have substantial extra-Scriptural evidence that it is, indeed, historically accurate! (Yes, even Genesis 1-11!) Since that wasn't the question, I won't attempt to go into detail here (and there are plenty of relevant Questions already on this SE), but it stands to reason that if it is accurate, those living at the time would have taught such to their children, and so on, such that the tradition at the time of Christ would match the fact of the OT's accuracy. Also, it seems likely that Jesus — who, being the very Word of God, would know for a fact that the OT is genuine history — would have corrected His disciples if they believed otherwise.
Further Reading