Jesus did not claim to be a manifestation of God. Jesus claimed to be the Son of God.
Jesus claim to be the Son of God and a messenger from God was backed up by God's enabling Jesus to perform miracles and by God raising Jesus from the dead.
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No, Jesus did not claim the title Manifestation of God. He claimed to be the Son of God since He came in the station of God's Son.
Even though Jesus never said He was a Manifestation of God, He did manifest God, by making God known and showing us what God is like.
John 1:18 - Bible Gateway
CEB No one has ever seen God. God the only Son, who is at the Father’s side, has made God known.
NASB No one has seen God at any time; the only begotten God who is in the bosom of the Father, He has explained
Him.
NCV No one has ever seen God. But God the only Son is very close to the Father, and he has shown us what God is like.
NLV The much-loved Son is beside the Father. No man has ever seen God. But Christ has made God known to us.
RSV No one has ever seen God; the only Son, who is in the bosom of the Father, he has made him known.
WE No one has ever seen God. But his only Son is very near to his Father's heart. He has told us plainly about God.
The term "Manifestation of God" seems to be specifically a Baha'i term and results from a redefinition of the word "Manifestation".
The Bible says that God was manifest in the flesh. To Baha'is that means that Jesus manifested God in the flesh.
That means that Jesus made God known to us and showed us what God is like, since Jesus was a mirror image of God.
1 Timothy 3-16
KJV
And without controversy great is the mystery of godliness:
God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory.