The first five books of the Bible were compiled by the same author, this includes Genesis. (all show Moses as the author and compiler by direct revelation also using the traditions i.e genealogies. Exod.17:14; Lev.1:1-2 Num.33:2; Deut.1:1). What God told Moses he wrote. He did not write anything God did not tell him to write. How did the writer (Moses) know what happened before man appeared? God revealed the past, as He reveals the future to the prophets.

It is always important to pay attention to details of any Scripture, especially the creation account in Genesis 1 and 2. These are not two contradictory accounts of creation. Genesis 1 covers the six days of creation. God pronounced it good at the completion of the sixth day. Genesis 2, from verse 4 onward, is a looking into the details of the events of Day 6, the origin of the human race. These accounts are not contradictory. Genesis (Hebrew Beresheeth-means in the beginning, titled by the first words) has a specific structure throughout its record, especially when it comes to the flood, the genealogies and the forming of  nations, giving geography and the generations of families from Adam through the flood (the taldot- generations) are specific in detail.

Genesis two gives us the details missing from Genesis 1. Romans 4:17: God, who…calls the things that are not, as though they were.” Hebrews 11:3 also states: “the worlds were framed by the word of God, so that what is seen has not been made of things which appear.”

God is presented as the Creator of both the material and the immaterial universe, of all things made. As John 1:2 tells us. Genesis 1:1 In the beginning God . God is introduced as Elohim (used thirty-five times), the Hebrew word for “God,” He is the Creator that existed before all things. It is in Genesis 2 that God is called YHWH Elohim, identifying him as the self existent one creator of both the heavens (plural) and the earth. The earth becomes the center of His plan and the sun, moon and stars are created in reference to the earth.

Gen 1:2-4 As the Spirit of God was hovered over the face of the waters. Then the first words God spoke, "Let there be light"; and there was light. And God saw the light, that it was good; and God divided the light from the darkness.”

The sequence is proportioned throughout this first chapter. Each of the six days begins the same way:  And God said as an introduction, (v. 3, 6, 9, 14, 20, 24). Then: Let there be. And the summation of the creating act  there was or and it was so.

The sequence of days began in darkness (which is called night). “there was evening and there was morning, followed by the number of the day. The light that appears before the sun, is not sunlight. This light is not to be confused with the establishment of the sun, moon, and stars. The main objection is that there is light prior to the sun as if God cannot produce another source of light without the sun. This is a unique light that provides light for the first three days until the luminaries of day (sun) and night (moon) appear on the fourth day. This light separated darkness, it was from the creator- most believe this to be  the first appearance of the Shekinah Glory, light as the visible manifestation of God's presence as he began creating. This is referred  in 2 Corinthians 4:6 states: Seeing it is God, that said, Light shall shine out of darkness…” 

The Hebrew writers did not have chapters at the time this was originally written so the creation account (Gen 1:24-31) actually concludes in Gen 2:1-3 “Thus the heavens and the earth, and all the host of them, were finished. And on the seventh day God ended His work which He had done, and He rested on the seventh day from all His work which He had done. Then God blessed the seventh day and sanctified it, because in it He rested from all His work which God had created and made.”

The beginning of Genesis 2 sums up the whole period of creation. Genesis 2:1: “Thus the heavens and the earth, and all the host of them, were finished.’ It begins with the finishing of creation which occurred on the 6^th day and then reflects back. Instead it is summarizing what is already written in chapter 1 with the completion of God resting (Gen.2:2-3).

Genesis 2 is not a day by day report in sequence. If so then it would make no sense from this opening statement of its completion. Genesis two is a more detailed explanation of the sixth day; the day that Adam and Eve were made.  The detailed recap is stated in Gen. 2:4, "This is the account of the heavens and the earth when they were created, in the day that the Lord God made earth and heaven." Then, Moses goes on to detail the creation of Chapter 2 covers what became of the heavens and the earth that was created by God.

Genesis 2:4 to 4:26 is sometimes labeled a “second creation story.” Critics often use their misinterpretation to insist on their being contradictions in the Bible. Or that there were two races of man, the first perished and God started all over. Genesis 2 does not say anything about the creation of the earth, the creation of the sun, moon, and stars, the creation of sea creatures; yet these are not different accounts. Reading the text carefully makes it clear Gen. 1 and 2 correspond to each other.

It starts with a reference to the condition of the earth (2:5–6) that corresponds to the early part of the third day in the first account (1:9–10), it focuses on the creation of man on the sixth day. It appears to contradict Genesis 1:9-13, which clearly states that plants were already growing. But this is not a contradiction, Genesis 1:9-13 is speaking about the world in general, where the earth brought forth grass, the herb - the trees. Verse 5 onward is specifically describing the Garden of Eden where there are no plants within as yet. God is developing the place where Adam and Eve will live. The key is where it says  there was no man to till the ground; (man was already created) .The context of v.5 is about Eden not the whole earth.
Gen 2:7 reflects back of the man formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living being.
As it states in Gen 2:8 The LORD God planted a garden eastward in Eden, and there He put the man whom He had formed.

Gen 2:4-7: In Genesis we have what is called the Law of Recurrence. Chapter 2, the 2nd block goes into more detail of the earlier segment. The Hebrews would write using a block of Scripture and would have certain parts repeated with more detail given on certain aspects of the event afterwards. This produces a pattern when put together fits perfectly with both records. In chapter 1 of Genesis, the whole creation is described in sequential order of events but in chapter 2, the author takes portions of chapter one and adds in the details of certain portions he focuses on. Chpt.1 God created man and woman, in chpt.2 gives the details of how he did that.

Chapter 2:5-25 fills in the details of the sixth day of Creation, as how Adam and Eve were created and the order of that creation in verses 7 thru 24 of Gen. 2. 

In Genesis 1:26-28 we are told man is made in the image of God but not how. Gen 2:7-8 tells us the details of God forming man of the ground. After God made the material part of man, He breathed the breath of life into him and he then became a living soul (Gen. 2:7). This portion explains the material part of man originated with the dust of the ground but the life of man comes from God. Man is unique as a living soul. The separation of the immaterial results in the material part of man becoming dead (Psalm 104:29; I King 17:21-22; Acts 2:27, 32).

Gen 2:15 God makes a garden in Eden and puts Adam in the eastern part of Eden to care over and keep it in order. He then instructs him about what trees to eat from and which to not eat from. Before God makes him a helper (on the 6th day) he brings all the creatures to Adam to name all the animals and birds V.18-19  is reflecting back at what he previously made before man. (Gen 1:24-25 explains the creatures made from the earth “according to its kind”) and has Adam name them before he puts him asleep (v.21) to operate on him to give him his wife. V. 19 “Out of the ground the LORD God formed every beast of the field and every bird of the air, and brought them to Adam to see what he would call them.” They were seen by Adam and named which brought the conclusion (according to chapter 1:24-26) that he needed a helper- his wife.

Gen 2:18-21 “And the LORD God said, "It is not good that man should be alone; I will make him a helper comparable to him." Out of the ground the LORD God formed every beast of the field and every bird of the air, and brought them to Adam to see what he would call them. And whatever Adam called each living creature, that was its name. So Adam gave names to all cattle, to the birds of the air, and to every beast of the field. But for Adam there was not found a helper comparable to him. And the LORD God caused a deep sleep to fall on Adam, and he slept; and He took one of his ribs, and closed up the flesh in its place.”

Some claim that Chapter 1 seems to say that the animals were created before man but in Chapter 2, man is described as being made first? It is not saying these animals were made after Adam- as if giving a sequence of events, but only how they were made as it reflects back and builds on the Genesis one account.

The animals and man were both created on the 6th day but they were made before man, as it says in Genesis 1:26 -27 Then God said, "Let Us make man in Our image, according to Our likeness; let them have dominion over the fish of the sea, over the birds of the air, and over the cattle, over all the earth and over every creeping thing that creeps on the earth." So God created man in His own image; in the image of God He created him; male and female He created them.”

Man and woman were made to have authority over the animals in a secluded garden God had made as a testing ground. What we see is the woman was in the mind of God, before God made her from Adam. Gen 1:26-27 (plural) “let them …He created him; male and female He created them.” Before man was created the woman was considered as part of man. That is an important concept, from the standpoint of typology as we learn in the New Testament of Christ and the church, as well as from the standpoint of humanity and the family unit. God formed Adam out of the dust of the ground (Adamah). Eve was made from the rib of Adam also from the dust same material as Adam, just twice removed. Chapter 2 fills in the details. Both man and woman are included -the details of how woman is taken from man and given back to him in marriage is described in chapter 2:21-23

What is focused on is man being alone without a mate, this is not giving a sequential order but making an overall statement of how he was given a wife.