There is another reason why I think Genesis 2:7 happened 1st, before man was made into the image and likeness of God as we see in Genesis 1:26-28. And because of this reason, I believe your statement which follows is in error, “When God first created man, alone, he was made in the image of God. Man did not need a wife to be made in the image of God, because God is three in one — not two as one.”
When you read Genesis 1:23-31, it shows us that the animals were created before Mankind was made into the image and likeness of God. Do you agree with this?
Chapter 2:18-20, however shows us more detail. In these verses we are told one of the purposes of why God made the animals. It was because God said it was not good for a man to be alone. So the process of finding the man a helper was set forth, with the creation of the animals, etc. The main point to keep in mind is that Genesis chapter 2 is showing us that Man was in existence before the creation of the animals, and in Genesis chapter 1, Man was not made into the image and likeness of God until after the creation of the animals. As we know, no helper was found for the Man from among the animals. Adam at this time while being alone, without the woman, was a living soul as in what Genesis 2:7 says. This we know for sure.
A suitable helper was found for Adam in Genesis 2:21-25. Genesis 2:21-25 is what is happening here in Genesis 1:26 and 27. This is when God decided to make Man into His image and likeness.
Genesis 2:18-24 says, “And the LORD God said, It is not good that the man should be alone; I will make him an help meet for him. And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof. And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him. And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof; And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man. And Adam said, This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man. Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.”
This passage is not saying that God made the animals to see if one of them could be a helpmeet for Adam. We are talking about God, the infinitely wise Creator. He is the One who made everything “according to his KIND.” Genesis 1:25-27 says, “And God made the beast of the earth AFTER HIS KIND, and cattle AFTER THEIR KIND, and every thing that creepeth upon the earth AFTER HIS KIND: and God saw that it was good. And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth. So God created man in his own image, in the image of God created he him; male and female created he them.” Animals are a different KIND than man. Man was made in the image of God — animals were not. God never confuses KINDS upon earth. They cannot interbreed, etc. I Corinthians 15:39 says, “All flesh is not the same flesh: but there is one kind of flesh of men, another flesh of beasts, another of fishes, and another of birds.”
Why was God bringing the animals to Adam? NOT to see if one would make a suitable helpmeet to him (God already knew that would be utter confusion, because they were different kinds). The passage gives the answer as to why God was bringing the animals to Adam, “and brought them unto Adam TO SEE WHAT HE WOULD CALL THEM.” God brought the animals to Adam to allow him to NAME them.
Throughout the passage the fact is stated, “I will make him an help meet for him,” “but for Adam there was not found an help meet for him,” because Adam was looking at all of these animals (which God created as male and female — they were all pairs), but Adam had no match for he himself, like all of the animals did. It is simply stating that Adam, unlike all of the animals, did not yet have a suitable mate — like all of the animals had for themselves.
When God created man, He created man in His image — unlike any of the animals. God did not grant man a different status or likeness once He created his helpmeet, woman. Genesis 1:26 says, “And God said, LET US MAKE MAN IN OUR IMAGE…” Genesis 1:27 says, “So GOD CREATED MAN IN HIS OWN IMAGE, in the image of God created he him…” Genesis 9:6 says, “Whoso sheddeth man’s blood, by man shall his blood be shed: for IN THE IMAGE OF GOD MADE HE MAN.”
I Corinthians 11:7 also clearly shows your conclusion to be wrong, “For A MAN indeed ought not to cover his head, forasmuch as HE IS THE IMAGE AND GLORY OF GOD: BUT THE WOMAN IS THE GLORY OF THE MAN.” When God created man, alone, He created him in the image of God.