Answer
The word Trinity is not used in the New Testament, but Christians believe that this term best describes God, who eternally exists as three distinct Persons. He has revealed Himself to us as Father, Son, and Holy Spirit (see Galatians 4:6). We often speak of the Trinity as the first Person, the Father; the second Person, the Son; and the third Person, the Spirit.
In no way do the terms first, second, and third, applied to the Persons of the Trinity, suggest levels of importance or significance. The wording of the Athanasian Creed was careful to maintain the equality of the Persons of the godhead: “We worship one God in Trinity, and Trinity in Unity, neither confounding the persons, nor dividing the substance. For there is one Person of the Father, another of the Son, and another of the Holy Spirit. But the godhead of the Father, of the Son, and of the Holy Spirit, is all one, the glory equal, the majesty co-eternal. . . . In the Trinity none is before or after another; none is greater or less than another, but all three Persons are co-eternal together and co-equal.”
While each Person of the Trinity is co-eternal and co-equal with the others ontologically, when the members of the Trinity relate to people, they do so in a specific hierarchy. That is, each Person of the Trinity plays a specific role. In the New Testament, when the term God is used, it most often refers to God the Father.
The Father is the “first Person of the Trinity” because in the “Trinitarian formula” found in Matthew 28:19, the Father is presented first: “Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit.” The simple word order of the formula might be enough to explain the Father’s position as “first.” However, there is more that contributes to the Father’s being the first Person of the Trinity.
The Father is also called “first” because He has first priority within the economic Trinity. This would be similar to how a human father is considered the head of a household. The Father sent Jesus into the world (John 6:57), and Jesus came in obedience to the Father and lived on earth in submission to the Father. “Very truly I tell you, the Son can do nothing by himself; he can do only what he sees his Father doing, because whatever the Father does the Son also does” (John 5:19). It is the Father who raised Jesus from the dead (Acts 2:32) and raised Him to the right hand of power, and it is the Father who will be glorified in the drama of redemption (Philippians 2:9–11).
So, the Father is the first Person of the Trinity because He is listed first and also, within the economic Trinity, He holds the place of leadership, like the father of a household.