If I remember correctly, the idea that Jesus became Christ at his baptism is referred to as the "Adoptionist Theory" and it has a long history. I believe that the idea comes from Psalms 2:5-7
5 Then will he speak to them in his anger, and in his fierce displeasure will he terrify them: 6 And *I* have anointed my king upon Zion, the hill of my holiness.
7 I will declare the decree: Jehovah hath said unto me, Thou art my Son; *I* this day have begotten thee.
Psalms 2:5-7 (Darby's)
It is also worth noting the different methods that the gospel writers use when describing the announcement
Matthew portrays it as an announcement to all present.
16 And Jesus, having been baptised, went up straightway from the water, and lo, the heavens were opened to him, and he saw the Spirit of God descending as a dove, and coming upon him: 17 and behold, a voice out of the heavens saying, This is my beloved Son, in whom I have found my delight.
Matt 3:16-17 (Darby's)
Mark portrays it as an announcement to Jesus.
10 And straightway going up from the water, he saw the heavens parting asunder, and the Spirit, as a dove, descending upon him. 11 And there came a voice out of the heavens: *Thou* art my beloved Son, in thee I have found my delight.
Mark 1:10-11 (Darby's)
Luke portrays it as a announcement to Jesus.
22 and the Holy Spirit descended in a bodily form as a dove upon him; and a voice came out of heaven, *Thou* art my beloved Son, in thee I have found my delight.
Luke 3:22 (Darby's)
In the book of John, The Son of God is revealed to John the Baptist.
33 And I knew him not; but he who sent me to baptise with water, *he* said to me, Upon whom thou shalt see the Spirit descending and abiding on him, he it is who baptises with the Holy Spirit. 34 And I have seen and borne witness that this is the Son of God.
John 1:33-34 (Darby's)
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