If the Old testament was sufficient, there would be no need for Jesus and the New Testament. But we have a New Testament, don't we?.
Anyway, it was believed Jesus was God long before Nicaea and Constantine
1. Ignatius of Antioch (c. 50–117): For our God, Jesus the Christ, was conceived by Mary according to God’s plan, both from the seed of David and of the Holy Spirit. (Ignatius, Letter to the Ephesians, 18.2. Translation from Michael Holmes, Apostolic Fathers, 197)
2. Ignatius (again): Consequently all magic and every kind of spell were dissolved, the ignorance so characteristic of wickedness vanished, and the ancient kingdom was abolished when God appeared in human form to bring the newness of eternal life. (Ibid., 19.3. Holmes, AF, 199)
3. Ignatius (again): For our God Jesus Christ is more visible now that he is in the Father. (Ignatius, Letter to the Romans, 3.3. Holmes, AF, 229)
4. Ignatius (again): I glorify Jesus Christ, the God who made you so wise, for I observed that you are established in an unshakable faith, having been nailed, as it were, to the cross of the Lord Jesus Christ. (Ignatius, Letter to the Smyrnaeans, 1.1. Holmes, AF, 249.)
5. Ignatius (again): Wait expectantly for the one who is above time: the Eternal, the Invisible, who for our sake became visible; the Intangible, the Unsuffering, who for our sake suffered, who for our sake endured in every way. (Ignatius, Letter to Polycarp, 3.2. Holmes, AF, 265.)
6. Polycarp of Smyrna (69–155): Now may the God and Father of our Lord Jesus Christ, and the eternal high priest himself, the Son of God Jesus Christ, build you up in faith and truth . . ., and to us with you, and to all those under heaven who will yet believe in our Lord and God Jesus Christ and in his Father who raised him from the dead. (Polycarp, Philippians, 12:2. Holmes, AF, 295)
7. Epistle of Barnabas (written c. 70–130): “If the Lord submitted to suffer for our souls, even though he is Lord of the whole world, to whom God said at the foundation of the world, “Let us make humankind according to our image and likeness,” how is it, then, that he submitted to suffer at the hands of humans?” (Epistle of Barnabas, 5.5. Holmes, AF, 393)
8. Justin Martyr (100–165): And that Christ being Lord, and God the Son of God, and appearing formerly in power as Man, and Angel, and in the glory of fire as at the bush, so also was manifested at the judgment executed on Sodom, has been demonstrated fully by what has been said. (Justin Martyr, Dialogue with Trypho, 128. Translation from Alexander Roberts and James Donaldson, Ante-Nicene Fathers, I:264)
9. Justin (again): “Permit me first to recount the prophecies, which I wish to do in order to prove that Christ is called both God and Lord of hosts.” (Ibid., 36. ANF, I:212.)
10. Justin (again): Therefore these words testify explicitly that He [Jesus] is witnessed to by Him [the Father] who established these things, as deserving to be worshipped, as God and as Christ. (Ibid., 63. ANF, I:229)
11. Justin (again): The Father of the universe has a Son; who also, being the first-begotten Word of God, is even God. And of old He appeared in the shape of fire and in the likeness of an angel to Moses and to the other prophets; but now in the times of your reign, having, as we before said, become Man by a virgin . . .” (Justin Martyr, First Apology, 63. ANF, I:184)
12. Justin (again): For if you had understood what has been written by the prophets, you would not have denied that He was God, Son of the only, unbegotten, unutterable God. (Justin Martyr, Dialogue with Trypho, 126. ANF, I:263)
13. Tatian (110–172): We do not act as fools, O Greeks, nor utter idle tales when we announce that God was born in the form of man. (Tatian, Address to the Greeks, 21. ANF, II:74)
14. Melito of Sardis (d. c. 180): “He that hung up the earth in space was Himself hanged up; He that fixed the heavens was fixed with nails; He that bore up the earth was born up on a tree; the Lord of all was subjected to ignominy in a naked body – God put to death! . . . n order that He might not be seen, the luminaries turned away, and the day became darkened—because they slew God, who hung naked on the tree. . . . This is He who made the heaven and the earth, and in the beginning, together with the Father, fashioned man; who was announced by means of the law and the prophets; who put on a bodily form in the Virgin; who was hanged upon the tree; who was buried in the earth; who rose from the place of the dead, and ascended to the height of heaven, and sitteth on the right hand of the Father.” (Melito, 5. ANF, VIII:757)
15. Irenaeus of Lyons (120–202): “For I have shown from the Scriptures, that no one of the sons of Adam is as to everything, and absolutely, called God, or named Lord. But that He is Himself in His own right, beyond all men who ever lived, God, and Lord, and King Eternal, and the Incarnate Word, proclaimed by all the prophets, the apostles, and by the Spirit Himself, may be seen by all who have attained to even a small portion of the truth. Now, the Scriptures would not have testified these things of Him, if, like others, He had been a mere man. . . . He is the holy Lord, the Wonderful, the Counselor, the Beautiful in appearance, and the Mighty God, coming on the clouds as the Judge of all men; — all these things did the Scriptures prophesy of Him.” (Irenaeus, Against Heresies, 3.19.2. ANF, I:449)
16. Irenaeus (again): “He received testimony from all that He was very man, and that He was very God, from the Father, from the Spirit, from angels, from the creation itself, from men, from apostate spirits and demons.” (Ibid., 4.6.7. ANF, I:469)
17. Irenaeus (again): “Christ Jesus [is] our Lord, and God, and Savior, and King, according to the will of the invisible Father.” (Ibid., 1.10.1. ANF, I:330)
18. Irenaeus (again): “Christ Himself, therefore, together with the Father, is the God of the living, who spoke to Moses, and who was also manifested to the fathers.” (Ibid., 4.5.2. ANF, I:467)
19. Clement of Alexandria (c. 150–215): “This Word, then, the Christ, the cause of both our being at first (for He was in God) and of our well-being, this very Word has now appeared as man, He alone being both, both God and man—the Author of all blessings to us; by whom we, being taught to live well, are sent on our way to life eternal. . . . . . . The Word, who in the beginning bestowed on us life as Creator when He formed us, taught us to live well when He appeared as our Teacher; that as God He might afterwards conduct us to the life which never ends” (Clement of Alexandria, Exhortation to the Heathen, 1. ANF, II:173)
20. Tertullian (c. 160–225): For God alone is without sin; and the only man without sin is Christ, since Christ is also God.” (Tertullian, Treatise on the Soul, 41. ANF, III:221)
21. Tertullian (again): “Thus Christ is Spirit of Spirit, and God of God, as light of light is kindled. . . . That which has come forth out of God is at once God and the Son of God, and the two are one. In this way also, as He is Spirit of Spirit and God of God, He is made a second in manner of existence—in position, not in nature; and He did not withdraw from the original source, but went forth. This ray of God, then, as it was always foretold in ancient times, descending into a certain virgin, and made flesh in her womb, is in His birth God and man united.” (Tertullian, Apology, 21. ANF, III:34–35)
22. Hippolytus (170–235): “The Logos alone of this God is from God himself; wherefore also the Logos is God, being the substance of God.” (Hippolytus, Refutation of All Heresies, 10.29. ANF, V:151)
23. Caius (180–217) [in response to those who would question the deity of Christ] “Perhaps what they allege might be credible, did not the Holy Scriptures, in the first place, contradict them. And then, besides, there are writings of certain brethren older than the times of Victor, which they wrote against the heathen in defense of the truth, and against the heresies of their time: I mean Justin and Miltiades, and Tatian and Clement, and many others, in all which divinity is ascribed to Christ. For who is ignorant of the books of Irenaeus and Melito, and the rest, which declare Christ to be God and man? All the psalms, too, and hymns of brethren, which have been written from the beginning by the faithful, celebrate Christ the Word of God, ascribing divinity to Him.” (Caius, Fragments, 2.1. ANF, V:601)
24. Origen (c. 185–254): “Jesus Christ . . . in the last times, divesting Himself (of His glory), became a man, and was incarnate although God, and while made a man remained the God which He was.” (Origen, De Principiis, Preface, 4. ANF, IV:240)
25. Novatian of Rome (210–280) “For Scripture as much announces Christ as also God, as it announces God Himself as man. It has as much described Jesus Christ to be man, as moreover it has also described Christ the Lord to be God. Because it does not set forth Him to be the Son of God only, but also the Son of man; nor does it only say, the Son of man, but it has also been accustomed to speak of Him as the Son of God. So that being of both, He is both, lest if He should be one only, He could not be the other. For as nature itself has prescribed that he must be believed to be a man who is of man, so the same nature prescribes also that He must be believed to be God who is of God. . . . Let them, therefore, who read that Jesus Christ the Son of man is man, read also that this same Jesus is called also God and the Son of God” (Novatian, On the Trinity, 11. ANF, V:620.)