Why are Adam and Eve considered married?

Simple answer - "Because God!"

In Genesis 1:27-28 God's involvement in the process is made clear:

• So God created mankind in his own image,in the image of God he created them; male and female he created them. God blessed them and said to them, “Be fruitful and increase in number; ...

And even clearer in Genesis 2. Thomas quoted the core of this, but the extra detail adds usefully to understanding the process:

Genesis 2: 18-24 (excerpts)

• The Lord God said, “It is not good for the man to be alone. ... But for Adam no suitable helper was found. ... Then the Lord God made a woman ... and he brought her to the man. The man said, “This is now bone of my bones and flesh of my flesh; she shall be called ‘woman,’ ... That is why a man leaves his father and mother and is united to his wife, and they become one flesh."

Korosia said:

These verses make it clear that God created man and woman, but I'm not seeing where it explains the connection between that event and a literal marriage between Adam and Eve.

You thought Thomas's answer explained it - but an expanded context example makes it less clear somehow? Yes? || In the NIV Genesis refers to Adam's wife 6 times. As Luke noted, the same word could be translated "woman" but it is still obvious that the context implies wife. For this to have happened then God's active involvement obviously made the difference.

It seems highly clear that when:

The Lord God said, “It is not good for the man to be alone. ... But for Adam no suitable helper was found. ... Then the Lord God made a woman ... and he brought her to the man.

as the other animals all had mates, that God is not 'just' meaning the woman is to be a 'helper'. You could try that interpretation, but I doubt that many would find it convincing. And,

The man said, “This is now bone of my bones and flesh of my flesh; she shall be called ‘woman,’ ...

This he says standing before God. Again, you could see that as Adam 'repurposing his helper into 'one flesh', without God intending it. I doubt that you could sell the idea :-)

That is why a man leaves his father and mother and is united to his wife, and they become one flesh."

Genesis 2:24 says a husband should be “joined” to his wife. Other translations say he should cling or cleave to her. Today we would say he should bond with her. Besides God, she should be his highest commitment.

Adam was joined to Eve implying marriage.

This can only be answered when one defines what it means to be married, and how one becomes married. (For a long long time in rural areas where there was no permanently stationed local priest, many people married one another by by "just" saying they were married, and behaving as if they were married.)

The Catechism of the Catholic Church, in the section about the sacrament of marriage, states:

1604 God who created man out of love also calls him to love the fundamental and innate vocation of every human being. For man is created in the image and likeness of God who is himself love. Since God created him man and woman, their mutual love becomes an image of the absolute and unfailing love with which God loves man. It is good, very good, in the Creator's eyes. And this love which God blesses is intended to be fruitful and to be realized in the common work of watching over creation: "And God blessed them, and God said to them: 'Be fruitful and multiply, and fill the earth and subdue it.'"

1605 Holy Scripture affirms that man and woman were created for one another: "It is not good that the man should be alone." The woman, "flesh of his flesh," his equal, his nearest in all things, is given to him by God as a "helpmate"; she thus represents God from whom comes our help. "Therefore a man leaves his father and his mother and cleaves to his wife, and they become one flesh." The Lord himself shows that this signifies an unbreakable union of their two lives by recalling what the plan of the Creator had been "in the beginning": "So they are no longer two, but one flesh."

Regarding your original concern, a secular vision of marriage as merely a human-made, institutionalised contract may try to deny marriage in Adam and Eve by pointing out the lack of an explicit contract. This is a total reversal of the actual logic of marriage. Marriage is the outcome of a blessing, of spouses subduing to God's will. The institutionalised contract is merely a reflection of this outcome.

In Mark 10:9 Jesus says, in the context of marriage, "What God has joined together, let not man separate." Clearly, when you read of the beginnings in Genesis, God brought Adam and Eve together. (Genesis 2: 18-24)

Genesis 2:24–25 (ESV): Therefore a man shall leave his father and his mother and hold fast to his wife, and they shall become one flesh. 25 And the man and his wife were both naked and were not ashamed.

Genesis pretty clearly views them as husband and wife, even giving their union as foundational to all other marriages.