There is a lot of talk, including in Scripture, about the meaning of man being made before woman. There is a lot to be considered there that impacts life, relationships, and family. But before you consider and debate all of those implications…
In the first creation account we simply get the statement that God mad humanity, male and female He made them. In that first account there is no distinction between the two halves of humanity other than they are both there in the creation of mankind. Female is a part—an important part of what it means to be human, So important, in fact, that we get this second account where God allows man to suffer in a “not good” situation for a long time. Long enough for him to realize that he is alone and incomplete.
It is at that point, when the man is suffering in his incompleteness, that God finishes the creation of humanity. And note here that God does not just create the woman. She is not a separate creation; a matching piece. She was already there in the essence of man. She is taken from man. She was already a part of him.
That is something we do not emphasize enough. Maybe it is seen as too obvious, but it merits spelling out. Women are people. Women are not just second-halves. Women are not just help-mates. Women are not just objects fulfilling a purpose subordinate to men. Women are not just sex. Women are individuals created to be in relationship with their Creator just as men are. Perhaps as Christians we need to spend a little less time emphasizing the dangers of women, how NOT to treat women, how NOT to look at women, and more time teaching men to see women as individuals.
This passage is less about the creation of woman and more about the completion of the creation of humanity.