The short answer: not really.
The long answer: There are two texts that might say that Jesus is God. John 1:1 and Rom 9:5. Let’s start with Rom 9:5. This text reads:
Theirs [the Jews] are the patriarchs, and from them is traced the human ancestry of Christ, who is God over all, forever praised! Amen.
However, the Greek is ambiguous. The text can also be translated:
Theirs [the Jews] are the patriarchs, and from them is traced the human ancestry of Christ. God who is over all, forever praised! Amen.
John is slightly more complicated. He clearly says that the Logos is God in 1:1, though he also says that the Logos was “with God”. Elsewhere he says that he and the Father are one (5:18) and that Christ is equal to the Father (10:30). So, I am willing to concede to a limited extent that John might consider Jesus to be God, except that he then commits the subordinationist heresy by saying that the Father is greater than Jesus (14:28).
Acts 2:36 says that Jesus was “made” Lord and Christ, though “Lord” in the NT is not necessarily the same as God. Col 1:15 says that he is the image (εικων) of the invisible God (του θεου του αορατου) (cf. 2 Cor 4:4). Of course, there is the Christ hymn in Phil 2. Verse 6 says:
Who, being in the form of God (εν μορφη θεου), did not consider it robbery to be equal with (or: like) God (ισα θεω).
Whatever that means. This phraseology is hotly debated, but suffice it to say that there is no clear parallel that would necessitate reading this passage as saying that Jesus was God. So, there is really very little to go on when considering whether or not the NT writers thought that Jesus was God. Of course, there is zero evidence that they were thinking in trinitarian terms, but I trust that my readers know to take that for granted.
So how then does Jesus become God in Christian tradition? It starts pretty early on (well, the mid-to-late second century) and really is basing itself on Logos theology. However, as Christians try to articulate this more and more, the question of Jesus’s nature keeps coming up. Is Christ divine as the docetists argued, or is Christ human, or is he some strange combination of the two? These debates continue until the Council of Chalcedon (Christ is fully human AND fully divine). Well, technically the debates continue for hundreds of years. Even today I am confident that less than 10% of Christians can supply an “orthodox” Christology (one of the reasons that I am annoyed that such a standard is used to exclude Mormons from Christianity. If most Christians are heretics of ignorance, why aren’t they considered non-Christians?)
Now, I know what you are all thinking: “Doesn’t Mormonism circumvent the problems of Chalcedon by getting rid of the metaphysical dualism between God and humanity?” Or perhaps you are saying to yourself, “Doesn’t the being/becoming dichotomy of classical philosophical theology produce a problem where there is not one? Don’t Mormon metaphysics of becoming solve this problem by denying a world of pure being?” Of course! For Mormons, Jesus is A God who is actualizing that potentiality through his mortality. We can point to the Luke 2:52 as an example of Christ who is becoming, not being, God.
While I completely agree that Mormonism solves the problem of the nature of Christ in the only philosophically satisfactory way, I am not sure that I am willing to say that the NT writers shared our metaphysics. But then again, Chalcedon’s “two natures” solution is even less biblical, so I wont worry about it too much.