Theophilus of Antioch (189 AD) is the earliest Christian to invoke the concept of "the Trinity:" and his version is not the Father, Son, and Holy Spirit, but rather "God, God"s Word (Christ), and God's Wisdom (not "the Holy Spirit1')."
From Athenagoras's Plea for Christians (ca. 177 AD):
"CHAP. X.--THE CHRISTIANS WORSHIP THE FATHER, SON, AND HOLY GHOST.
That we are not atheists, therefore, seeing that we acknowledge one God, uncreated, eternal, invisible, impassible, incomprehensible, illimitable, who is apprehended by the understanding only and the reason, who is encompassed by light, and beauty, and spirit, and power ineffable, by whom the universe has been created through His Logos, and set in order, and is kept in being--I have sufficiently demonstrated. [I say "His Logos"], for we acknowledge also a Son of God. Nor let any one think it ridiculous that God should have a Son. For though the poets, in their fictions, represent the gods as no better than men, our mode of thinking is not the same as theirs, concerning either God the Father or the Son.
But the Son of God is the Logos of the Father, in idea and in operation; for after the pattern of Him and by Him were all things made, the Father and the Son being one. And, the Son being in the Father and the Father in the Son, in oneness and power of spirit, the understanding and reason (nous kai logos) of the Father is the Son of God. But if, in your surpassing intelligence, it occurs to you to inquire what is meant by the Son, I will state briefly that He is the first product of the Father, not as having been brought into existence (for from the beginning, God, who is the eternal mind [
nous], had the Logos in Himself, being from eternity instinct with Logos [
logikos]; but inasmuch as He came forth to be the idea and energizing power of all material things, which lay like a nature without attributes, and an inactive earth, the grosser particles being mixed up with the lighter. The prophetic Spirit also agrees with our statements. "The Lord," it says, "made me, the beginning of His ways to His works."
The Holy Spirit Himself also, which operates in the prophets, we assert to be an effluence of God, flowing from Him, and returning back again like a beam of the sun. Who, then, would not be astonished to hear men who speak of God the Father, and of God the Son, and of the Holy Spirit, and who declare both their power in union and their distinction in order, called atheists? Nor is our teaching in what relates to the divine nature confined to these points; but we recognise also a multitude of angels and ministers, whom God the Maker and Framer of the world distributed and ap pointed to their several posts by His Logos, to occupy themselves about the elements, and the heavens, and the world, and the things in it, and the goodly ordering of them all."
Athenagoras of Athens: A Plea for the Christians
Matthew's tripartite baptismal f ormula does not use the tern "Trinity."
No, and that doesn't matter. What matters is that that "name" is singular in reference to three distinct "persons."
