This is a very deep subject! And, it is so simple!
'They' had 'no sin'!
Therefore, why would they need to be 'covered'?
Continue to follow this, and you will be able to understand the Bible!
Very important! The 'Woman' did not have a name!
Maintain the timeline!
Gen 5:2 Male and female created he them; and blessed them, and called their name Adam, in the day when they were created.
Gen 2:23 And Adam said, This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man.
Gen 2:24 Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.
It was pre-determined that Man, and Woman were equal when they were created! God took a rib, and 'cloned' the woman! The 'Woman' taken from the Man's 'side' is 'crystal clear' that she belongs 'right by his side'! Not, in front of him, and not behind him! The Woman is equal!
God, the father did not leave them without a remedy! He prophesied his son coming as a Lamb of God! The first prophecy, the oldest of all, had been given by God at the time of Adam and Eve’s sin: The serpent would bruise the seed of the woman. Prophesied: “And I will put enmity between you and the woman, and between your seed and her Seed; He will bruise your head, and you shall bruise His heel” (Gen. 3:15). Fulfilled: “ ‘Now is the judgment of this world. Now shall the prince of this world be cast out. And if I be lifted up from the earth, I will draw all to Myself.’ But He said this to signify by what death He was about to die” (John 12:31-33).
Gods' Word is beautiful when one 'studies it'!
The second 'sin' entered into the world, 'they' knew they were 'naked'! They had no righteousness covering them! This is very deep! Gen 3:8 And they heard the voice of the LORD God walking in the garden in the cool of the day: and Adam and his wife hid themselves from the presence of the LORD God amongst the trees of the garden. God, the father could not 'see them'! Sin separates us from God!
Gen 3:9 And the LORD God called unto Adam, and said unto him, Where art thou?
Do not believe they were playing hide, and seek! Peek a boo!
Verses that show sin separates us from God:
Isa 59:2 But your iniquities have separated between you and your God, and your sins have hid his face from you, that he will not hear.
Psa 66:18 If I regard iniquity in my heart, the Lord will not hear me: