Many trinitarians misinterpret this passage as all the “three persons” of the so-called trinity being manifested at once. But the Bible very clearly says that the voice and the dove were just a sign for John the Baptist to identify the Messiah. Because even though John and Jesus were cousins, they never met each other till the baptism.
John 1: 33 And I knew him not: but he that sent me to baptize with water, the same said unto me, Upon whom thou shalt see the Spirit descending, and remaining on him, the same is he which baptizeth with the Holy Ghost. 34 And I saw, and bare record that this is the Son of God.
Matt 3:16 … he saw the Spirit of God descending like a dove, and lighting upon him: 17 And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased.
Moreover, the Spirit of God came “like” a dove, not a real dove. The invisible Spirit took the form of a visible dove so that John would be able to identify the Messiah. Also, the Bible says that God is Omnipresent. He is able to present Himself everywhere at the same time. The voice from Heaven only lends further credibility to this statement, rather than implying that a separate person spoke from Heaven.
Also, the Bible records a similar incident of a voice from Heaven during the transfiguration. Once more, the scripture says that it was for a witness to the glory of Christ.
2 Pet 1:16 For we have not followed cunningly devised fables, when we made known unto you the power and coming of our Lord Jesus Christ, but were eyewitnesses of his majesty. 17 For he received from God the Father honour and glory, when there came such a voice to him from the excellent glory, This is my beloved Son, in whom I am well pleased. 18 And this voice which came from heaven we heard, when we were with him in the holy mount.
The Bible says "like" a dove not "as" a dove; the shape "like" a dove; not of a dove.
The Holy Spirit didn't come as a dove, but resembled the form of the dove in that the Holy Spirit descended as a dove does with wings.
Matthew 3:16 And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him:
See also Mark 1:10 And straightway coming up out of the water, he saw the heavens opened, and the Spirit like a dove descending upon him:
In the King James Version it even says in a shape "like" a dove, not as a dove.
Luke 3:22 And the Holy Ghost descended in a bodily shape…
I don't believe the Holy Spirit took the form of a dove, but descended like a dove descends.