When a man and a woman marry, they make oaths not just to each other, but also to God. That’s why Malachi says God is the witness against men who have broken faith with the wives of their marriage covenant (see Mal 2:14). Prior to modern times, marriages were customarily arranged (and still are in some cultures). The agreement between the two families typically included some financial arrangements and was sufficient to establish the marriage covenant. Today, a man and a woman are married when they make marriage vows that are witnessed not only publicly by the wedding guests, but also by God himself.
Sex is not technically necessary to create marriage—Joseph did not have sexual relations with Mary until after Jesus’ birth, yet Matthew says they were married (see Mt 1:24–25). But apart from exceptional circumstances, Scripture does not picture marital union without the consummation of physical-sexual union. The beautiful erotic imagery of Genesis 2:24–25 is unambiguous: Marriage is a “one-flesh” relationship.
Sexual union expresses, reinforces and reenacts the marital covenant. This explains the beautiful Hebrew euphemism for marital sex: to know (see Ge 4:1, translated made love). Adam, who was given Eve as his life companion, could continue to express and reenact their union by “knowing” Eve sexually. Sex does not create marriage, but sex is designed for marriage.