|Rabbi Shimon said: Why does the Torah say, "When a man will take a woman," and not "When a woman will be taken to a man"? This is because it is the way of a man to go seek a wife, but it is abnormal for a woman to go seek a husband. This is akin to
someone who loses something. Who is the one searching for the object? Obviously
the owner seeks to find his lost object. [And since the woman was created
from the man's lost bone, it is he who searches for her.]
The Mishnah Halachos asks: Why is
a man required to give the woman money for betrothal; she is his lost bone!?
When one takes back an article that he had lost, is he required to make a new kinyan?
He answers: If the man would know
for certain that the woman he is about to marry is his proper match from the
Days of Creation, it would not be necessary for him to make a new kinyan.
However, since this matter is uncertain to us, witnesses are required, and once
this transpires, the other people in the world give up hope from marrying this
woman, and she becomes the rightful wife to this man.
Accordingly, it can be said that
when Adam married Chavah, when there was no alternative woman, and she
obviously was destined to be his wife, it would not have been necessary to have
witnesses or any kinyan for that marriage.