The effect of Adam and Eve's sin on them
Sin put man out of harmony with his Creator. It thereby damaged not only his relations with God but also his relations with the rest of God’s creation, including damage to man’s own self, to his mind, heart, and body. It brought consequences of enormous evil upon the human race.
The conduct of the human pair immediately revealed this disharmony. Their covering portions of their divinely made bodies and thereafter their attempting to hide themselves from God were clear evidences of the alienation that had taken place within their minds and hearts. (Genesis 3:7, 8)
Sin thus caused them to feel guilt, anxiety, insecurity, shame. This illustrates the point made by the apostle at Romans 2:15, that God’s law was ‘written on man’s heart’; hence a violation of that law now produced an internal upheaval within man, his conscience accusing him of wrongdoing. In effect God, responding to the man’s excuse for his changed attitude toward his heavenly Father, promptly inquired: “From the tree from which I commanded you not to eat have you eaten?” — Genesis 3:9-11.
To be true to Himself, as well as for the good of the rest of his universal family, God could not countenance such a sinful course, on the part of either his human creatures or the spirit son turned rebel. Maintaining his holiness, he justly imposed the sentence of death on them all. The human pair were then expelled from God’s garden in Eden, hence cut off from access to that other tree designated by God as “the tree of life.” — Genesis 3:14-24.
Were Adam and Eve set up to fail?
Regarding God’s creation, including the first humans on earth, the Genesis account says: “God saw everything he had made and, look! it was very good.” (Genesis 1:31) Adam and Eve were perfectly made, ideally suited to their earthly environment. There was nothing deficient in their makeup. Created “very good,” they were certainly capable of the good conduct that was required of them. They were created “in God’s image.” (Genesis 1:27) So they had the capacity to demonstrate to some degree the godly qualities of wisdom, loyal love, justice, and goodness. Reflecting such qualities would help them to make decisions that would benefit them and bring pleasure to their heavenly Father.
God endowed these perfect, intelligent creatures with free will. So they were by no means preprogrammed to please God—like some sort of robot. Think about it. Which would mean more to you—a gift that is given mechanically or one that comes from the heart? The answer is obvious. Likewise, if Adam and Eve had freely chosen to obey God, their obedience would have meant all the more to him. The capacity to choose enabled the first human pair to obey God out of love.—Deuteronomy 30:19, 20.
Adam and Eve's sin - not an accident nor an unfortunate mishap
Since Adam and Eve were created perfect and since God’s command to them to not eat from the "tree of knowledge good and evil" was explicit and understood by both, it is evident that their sinning was willful and deliberate and therefore inexcusable. God’s words to them afterward offered no invitation to repent. (Genesis 3:16-24)
A footnote to Genesis 2:17 in The New Jerusalem Bible states that Adam and Eve laid claim “to complete moral independence by which man refuses to recognize his status as a created being . . . The first sin was an attack on God’s sovereignty.”
God’s law states that “the wages sin pays is death.” (Romans 6:23) Rather than hide this law from Adam, God told him that the penalty for disobedience would be death. (Genesis 3:3) When Adam sinned, God, “who cannot lie,” kept his word. (Titus 1:2) Adam passed on to his descendants not only sin but also the wages of sin—death.
Although sinful humans deserve the penalty of death, God extended to them “the riches of his undeserved kindness.” (Ephesians 1:7) His provision to redeem mankind—sending Jesus as a perfect sacrifice—was both profoundly just and supremely merciful. Being created in perfection and in ideal conditions was God's undeserved kindness given to Adam and Eve upon their creation as perfect humans under perfect conditions. They rejected this undeserved kindness by deliberately and willingly disobeying God, and thus forfeited any subsequent undeserved kindness that was given to their offspring through Jesus' perfect ransom sacrifice. It was profoundly just and loving by God to provide for this sacrifice for Adam and Eve’s offspring, as they were born into sin through no fault of their own.
Adam and Eve's response to their sin gives some further indication of their mental attitude towards the incident. “The woman whom you gave to be with me, she gave me fruit from the tree and so I ate,” said Adam (Adam blamed God for his own mistake). “The serpent—it deceived me and so I ate,” responded Eve (Eve deflecting the blame for her mistake to the Serpent). Those words, spoken to God by our first human parents, marked the beginning of mankind’s long history of making excuses and avoiding accountability - both clear signs of feeling sorry for the consequences but not repenting from their own behavior that led to it.—Genesis 3:12, 13.
In addition to that, being divinely commissioned and being the earthly head through whom God communicated instructions to the human family, Adam was God’s representative on earth. (Genesis 1:26, 28; 2:15-17; 1 Corinthians 11:3) Those serving in such capacity are said to ‘minister in God’s name’ and ‘speak in his name.’ (Deuteronomy 18:5, 18, 19; James 5:10) Thus, while his wife Eve had already profaned God’s name by her disobedience, Adam’s doing so was an especially reprehensible act of disrespect for the name he represented.
They actually both committed thus —due to their status as perfectly created representatives of God, and the ideal conditions they were in— blasphemy against the holy spirit, of which Jesus said that such a sin would not be forgiven. (Matthew 12:31-32)
For it is impossible to restore again to repentance those who have
once been enlightened, and have tasted the heavenly gift, and have
shared in the Holy Spirit, and have tasted the goodness of the word
of God and the powers of the age to come, and then have fallen away,
since on their own they are crucifying again the Son of God and are
holding him up to contempt. (Hebrews 6:4-6 - NRSV)
Adam and Eve were created enlightened, they not only tasted but were able to indulge in the heavenly gift of dwelling with God more than any other human being (besides Jesus), they shared in the holy spirit, they experienced goodness which God will restore in the future. But despite all that, they have fallen away - it is impossible for them to be restored to repentance (not even "again" as they weren't in need of repentance before their sin - they were in a state that didn't need saving, but only sustaining, which is why the "tree of life" was in the garden of Eden, and they were separated from it).
What about the arguments of faith displayed by Adam and Eve after their sin?
Did God's covering of Adam and Eve by animal skin prove he had thereby covered their sin by slaughtering animals?
First: The bible doesn't say that God "slaughtered" animals to get their skin of. He is the creator - what would have held him from miraculously providing the skin without the need of slaughtering animals?
Second:
God is kind and considerate toward all, including “the unthankful
and wicked.” (Luke 6:35) For instance, God “makes his sun rise on
both the wicked and the good and makes it rain on both the righteous
and the unrighteous.” (Matt. 5:45) Hence, even those who do not
acknowledge God as their Creator still benefit from his kind
provisions for life and may enjoy a measure of happiness.
We find an outstanding example of kindness in what God did for
Adam and Eve. Shortly after they sinned, Adam and Eve “sewed fig
leaves together and made loin coverings for themselves.” However,
God knew that they would need suitable clothing in order to live
outside of Eden, where the ground was now cursed with “thorns and
thistles.” So God kindly responded to their need by making “long
garments from skins” for them.—Gen. 3:7, 17, 18, 21.
Kindness - A quality expressed in word and action
Also the utterance of Eve when giving birth to Cain, apparently thanking the LORD (Genesis 4:1), doesn't prove Eve's repentance. Eve could validly say that Cain was produced “with the aid of the LORD” because God had not taken away the reproductive powers of sinful Adam and Eve and because, when passing judgment on her, God had said that she would “bring forth children,” though it would be with birth pangs.— Genesis 3:16
Did Eve have in mind that she might be the foretold woman who would produce the seed by means of which deliverance would come? (Genesis 3:15) If so, she was greatly mistaken. (Revelation 12:1) Deliverance would come through Jesus - he is the seed. (Revelation 12:5,6) The serpent is Satan - called the "original serpent" in Revelation 12:9 and 20:2. Satan's/the Serpent's head would be "crushed" eventually by Jesus who would bring the Devil to "nothing" (Hebrews 2:14). I will not go into the full exegesis of Genesis 3:15 here, as it would make this answer much longer than it already is. It suffices to say that Genesis 3:15 has nothing to do with Eve!
"What about Cain and Abel - they offered a burnt sacrifice to God - they surely must have learned this from Adam and Eve!"
The bible doesn't show a single occurrence where Adam or Eve gave burnt offerings to God. How would Cain and Abel deduce that offerings would be a suitable gift to God then?
Think about this - Cain and Abel certainly had visibility on God's cherubim guarding the entrance to the Garden of Eden with a flaming sword. (Genesis 3:24) Furthermore, God remained in contact with the first humans and their offspring as He was interested in their survival and becoming many, as he still wanted them to "fill the earth" (Genesis 1:28) and also that true faith would be cultivated among humans because God "wishes all to know the truth... and to be saved" (1. Timothy 2:4)!
So Cain and Abel knew about their parent's sin and understood why they were outside of Eden. They must have had conversations with God. They must have understood that even though they were no longer perfect and would have to eventually face death, their lives were a gift from God.
Their offerings indicated a recognition of their alienated state and of their desire for God’s favor.
Ever wondered why Cain got aware that God liked Abel's burnt offering more than his? And why was Cain not surprised to hear God speaking to him? (Genesis 4:2) - I reckon that they conversed regularly.
So there is no explicit biblical proof that Adam and Eve did anything that would indicate their true repentance and faithfulness to the end of their lives.
I'm not saying that I have not missed something from the Bible - my interpretation is not infallible, nor am I the judge. But it looks to me that Adam and Eve have ended up in the lake of fire (Gehenna) based on the information available in the Bible.
