Is Jesus an incarnation of God?
This is a trick question. Answering this wrong will make you a heretic. However, the answer is not binary: it is not completely wrong, but not completely correct. The premise of the question is already wrong, as this is a theology question, which tries to understand God from a manmade perspective rather than from what God says about himself.
Why is it not wrong to say that Jesus is an incarnation of God? John 1 says,
1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was in the beginning with God. 3 All things were made through him, and without him was not any thing made that was made. … 14 And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth.
Is this incarnation? Incarnation means “into flesh” so we can say “the Word was God” and “the Word became flesh” appear to fit the definition. However, Jesus is not merely the Word became flesh, for he has many roles.
In particular, Jesus says, “I am the way, and the truth, and the life. No one comes to the Father except through me” (John 14:6). We can all speak freely to the Son as a friend and not as a servant, but in the Old Testament, God only speaks through prophets and priests, who are descendants of Aaron (brother of Moses) belonging to the tribe of Levi. Jesus the only Son is the only way we get access to God the Father.
This is also why it is not completely correct to say that Jesus is an incarnation of God. The problem lies with the meaning of the word “incarnation” itself. In many religions, their gods incarnate by disguising themselves in human form but kept the same identity. Greek gods Zeus and Hermes took on human form in disguise to test who is hospitable. Hinduism believes that Siddhartha Gautama Buddha is an incarnation of the god Vishnu, a view that Buddhists disagree. Tibetan Buddhism believes that Dalai Lama repeatedly reincarnates throughout many lifetimes as different persons but with the same spiritual lineage.
The idea of incarnation usually preserves the identity of the deity, but most mainline Christians agree that the Father, the Son, and the Holy Spirit have distinct identities in the Holy Trinity. This distinction is part of God’s salvation plan. Just giving a binary answer to this theological question does not help us understand why Jesus came into the world.