Where in the Bible does it say or indicate that a man and a woman have to be married? Adam and Eve coexisted there was no ceremony.
One does not have to marry, but if one wants to have sex, then he must marry.
"But I say to the unmarried and to the widows: It is good for them if they remain even as I am; but if they cannot exercise self-control, let them marry. For it is better to marry than to burn with passion" (I Corinthians 5:8-9).
"Marriage is honorable among all, and the bed undefiled; but fornicators and adulterers God will judge" (Hebrews 13:4).
The fact that sex outside of marriage is a sin (fornication) is sufficient proof that one must be married to have sex and remain righteous. "Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived. Neither fornicators, nor idolaters, nor adulterers, nor homosexuals, nor sodomites, nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners will inherit the kingdom of God" (I Corinthians 6:9-10).
In regards to Adam and Eve, it was God who brought them together. And Jesus pointed out that they were married. "And He answered and said to them, "Have you not read that He who made them at the beginning 'made them male and female,' and said, 'For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh'? So then, they are no longer two but one flesh. Therefore what God has joined together, let not man separate" (Matthew 19:4-6). The marriage is when a man is joined to his wife. That joining is in the covenant a man makes with a woman. "Yet she is your companion and your wife by covenant" (Malachi 2:14).