The doctrine of the Trinity simply states that God consists of three persons in one essence. The three persons are the Father, Son, and Holy Spirit. In Matthew 3:16-17, all three are present at the same time and in the same place. So, do these verses support the doctrine of the Trinity or do they instead point to tritheism, the idea that there are three distinct and separate gods (the position of Mormons)?
Michael Wilkins, writing in The Gospels and Acts (The Holman Apologetics Commentary on the Bible), argues that tritheism is not supported by the totality of the biblical witness.
At this early date of Jesus’ ministry, Matthew is only hinting at what will later be made clearer in his Gospel and in the rest of the NT— that there is one God, but within that oneness of essence there are three persons: Father, Son, and Holy Spirit. Tritheism is certainly not a biblical option. The OT repeatedly affirms that there is but one God: ‘Listen, Israel: The Lord our God, the Lord is One’ (Deut 6: 4), and both Jesus and the apostles repeat this truth (Mark 12: 29; 1 Cor 8: 4, 6). Likewise, Jesus will emphasize the divine nature of Father, Son, and Spirit, and Matthew will begin pointing to this stupendous truth.
As Morris states, ‘Matthew has certain trinitarian interest’ (Morris 1992, 68). Matthew concludes his Gospel with another trinitarian allusion in Jesus’ instruction that new disciples are to be baptized in the singular name of the Father, Son, and Holy Spirit (28: 19). This is the oneness of God in three personal distinctions.
Matthew lays out a clear picture of Jesus’ deity by drawing upon OT prophecies. Prior to the incarnation, the strong divine language of some of the prophecies could not be adequately understood, leading to diverse views concerning the nature of the Messiah (see Kaiser 1995). But for Matthew, the reality of the incarnation now makes clear God’s revelation through the prophets: Jesus is God the Son, who is in vital relationship with his Father God, in the power of the Spirit of God. That all three members of the godhead share the same essence does not lead to an expectation that they cannot be present and active in the same scene. If they could not simultaneously participate in a scene such as this, they would in fact not be three persons.
Norman Geisler and Ron Rhodes add in When Cultists Ask:
Matthew 3:16–17 supports the doctrine of the Trinity, though in itself it does not prove the doctrine. Trinitarians base their understanding of the nature of God on the accumulative evidence of the whole of Scripture. Taken by itself, all that the passage proves directly is that there are three different persons in the Godhead. It does not show that these three persons all share one and the same divine essence. . . .
Scripture taken as a whole yields the doctrine of the Trinity that is based on three lines of biblical evidence: (1) evidence that there is only one true God; (2) evidence that there are three Persons who are recognized as God; and (3) evidence for three-in-oneness within the Godhead. Scripture uniformly teaches that there is only one God (Deut. 6:4; 32:39; 2 Sam. 7:22; Ps. 86:10; Isa. 44:6; John 5:44; 17:3; Rom. 3:29–30; 16:27; 1 Cor. 8:4; Gal. 3:20; Eph. 4:6; 1 Thess. 1:9; 1 Tim. 1:17; 2:5; James 2:19; 1 John 5:20–21; Jude 25). Yet Scripture also calls three persons God—the Father (1 Peter 1:2), the Son (John 20:28; Heb. 1:8), and the Holy Spirit (Acts 5:3–4). Scripture also indicates three-in-oneness in the Godhead (Matt. 28:19; 2 Cor. 13:14). The accumulative evidence of the whole of Scripture indicates that God is a Trinity.