Did God's nature or attributes change by virtue of the Son's incarnation?

Every good thing given and every perfect gift is from above, coming down from the Father of lights, with whom there is no variation or shifting shadow.

-James 1:17

For I, the Lord, do not change; therefore you, the sons of Jacob, have not come to an end.

-Malachi 3:6

From what I can read, the incarnation wasn't a fact-finding mission. The word dwelt among us in order to bring about salvation.

Therefore, since the children share in flesh and blood, He Himself likewise also partook of the same, so that through death He might destroy the one who has the power of death, that is, the devil, 15 and free those who through fear of death were subject to slavery all their lives. 16 For clearly He does not give help to angels, but He gives help to the descendants of Abraham. 17 Therefore, in all things He had to be made like His brothers so that He might become a merciful and faithful high priest in things pertaining to God, to make propitiation for the sins of the people.

-Hebrews 2:14-17

It depends on what you mean by "change".

Irrespective of whether you are trinitarian or not, Malachai 3:6 says "I the Lord do not change" (NIV). God does not change in his purpose or his standards. He has never compromised on matters of morality, established by him.

However, there are examples in the scriptures that show, even prior to Jesus time on earth, that God is willing to adapt and change his means of achieving his purpose. Consider the account at Genesis 18 where Abraham 'persuades' God to spare Sodom if he were to find 10 righteous there. God listened to Abraham's reasoning and agreed to it.

It is a common claim of higher critics of the Bible that the 'old testament God' is different to the 'new testament God'. Really, any supposed differences could be illustrated by the changing relationship between parent and child. A parent may have consistent standards, yet change the way that they deal with their children over time as they grow.

Jesus' life as a human - whether you believe in the trinity or not - did contain 'new' experiences. God created humans so he knows that physical creation has the capacity to feel pain, but Jesus actually experienced that physical pain first-hand at his death. It could be argued that this would make him more compassionate, but really his actions throughout his life proved beyond any doubt that he already had the greatest compassion possible for humans, so arguably Jesus did not have a "change" in his personality or attributes for the experience - it was just an affirming experience.

The short answer is no. Philippians 2 explains it starting at vs5, "Have this attitude in yourselves which was also in Christ Jesus, Vs6, who, although (means in spite of the fact) He existed (or having existed) in the form of God, did not regard equality with God a thing to be grasped."

In other words, The Son of God had voluntarily took upon himself the form of a servant and the likeness of a man and submitted himself to the Father in that form thereby "foregoing" (or not clinging) to His innate divinity and powers associated with that divinity.

As a man who was submitted to the Father, he had received authority for all that he did, including raising from the dead. As a man, Jesus did not get special things that weren't already his before his incarnation.

So, Jesus went from one form of being God and took on another form of a bond-servant/man. Vs7-8, "but emptied Himself, taking the form of a bond-servant, and being made in the likeness of men. And being found in appearance of a man, He humbled Himself by becoming obedient to the point of death, even death on a cross."

This also means Jesus had two natures. One of deity on His Father's side and human on His mother's side. This is why Jesus oftentimes referred to Himself as the "Son of Man" and as the "Son of God."

Moreover, Jesus was not created but rather He was "SENT" from heaven. Please read John 3:13, John 6:42, John 6:41, John 6:48, John 6:50-51, John 6:58, Ephesians 4:9-10, At Hebrews 10:5, "Therefore when He comes into the world, He says, "Sacrifice and offering Thou hast not desired, But a body Thou hast prepared for Me."

Lastly, and as a side note? What is it about the Trinity that your confused about?

You are not the only one to be confused by the doctrine of the trinity! It must be the deepest doctrine there is, and so it was not put into a strict form of words till long after the last New Testament book had been written. Yet there is enough in the Bible to make sense of it. And that applies to this aspect of the Godhead which you ask about - whether God's nature or attributes changed by virtue of the Son's incarnation.

Here is a quotation from a book by a trinitarian Christian, giving pointers for you to think about, so that you might see the need to re-evaluate what the words 'nature' and 'attributes' mean with regard to the way God and Christ relate, in the Godhead.

"In the nature of what Deity is, that nature is possessed by a Person, who is named Jesus Christ. He shares that nature with his Father. In relationship – regarding person – his Father is greater than he. But in the matter of nature – eternal nature – his nature is equal to that of the Father and he is perfectly one with the Father. As well as this, Jesus Christ, born of woman, also possesses human nature.

The Divine relationship is within one Spirit – the Divine Person who is the Holy Spirit. All that passes between the Father and the Son – and between the son and the Father – does so in one Spirit. That Spirit is a Divine Person sharing the same divine nature as the Father and the Son.

Fulness is one of the attributes of Deity. And since that attribute is shared, then it follows that there must be – and there indeed is – a perfection of unity within Deity. For each shares the attribute of fulness. Everything – absolutely everything – is filled by Deity. By all that is Deity. Thus, there is – absolutely – a shared perfection of unity. In all things. This is sheer logic.

Only once was that perfect bond within Deity ever broken… “My God, my God – why hast thou forsaken me?” This appalling breach within everlasting Deity was caused by the bearing of sins. And by the resolving of the matter of sin, by means of death. This – the awful rift in the most perfect of relationships – was accepted and agreed upon by Deity in unanimous counsel, before the earth was created, for it was foreseen by the wisdom of Deity that it would be necessary. And yet Deity still created humanity. What revelation this is : it is wonderful!" (The Everlasting Gospel p 43, Nigel Johnstone, Belmont Publications 2017)

This means that you could summarise the trinity doctrine as, Three Persons sharing the divine nature; the Father and the Son share the one, divine nature, with absolute unity of the Spirit in that nature.

Given that absolute unity of the Holy Spirit with all three Persons, there could be no change to that divine nature with all its attributes, so that the answer to your question is, "No".

However, if you wish to delve more deeply into the intricacies of how, for instance, human nature can be tempted, but divine nature cannot be tempted, I recommend the answer to a Stack Bible Hermeneutics question, by the author of the book I've just quoted from : https://hermeneutics.stackexchange.com/questions/66876/jesus-was-tempted-but-god-cannot-be-tempted-how-then-do-we-reconcile-james-1/66877#66877