In the Hebrew Bible, a marriage ceremony is never actually described.
Priests and their attendants (Kohanim and Levites) are responsible for work in the sanctuary, such as sacrifices and offerings, so although they're the people "consecrated to God" and act as intermediaries between the people and God, they don't have any part in helping a man and woman form a permanent union as "one flesh" and become husband and wife.
In Genesis, a union between man and woman is described as just a commitment that two people make to live together, help each other, "be fruitful and multiply." Isaac brought Rebecca "into his tent," and she became his wife, so in their case, marriage is initiated between a couple when they engage in sex. Afterwards, they are understood as being bound to each other, and thus living in a marriage. This is understandable, since biblical times had a very different view of sex than what we see in modern society.
This is why I ask about the difference between what a wife is and what a concubine is in biblical times. Since a marriage ceremony is never described in the Bible, what qualities would make a concubine different than a wife?
Those are two different labels, so is it just suggesting a social status difference? A handmaid, even if she took up permanent residence with one man, would never be a "wife", only a "concubine"?
Bilhah and Zilphah are described as Jacob's "concubines", and Rachel and Leah are described as "wives", although the children from all four women are equal since they all become the twelve tribes. So why not call Rachel and Leah's handmaids wives?