Were Adam and Eve doomed to hell since they sinned in the Garden or were Adam and Eve saved?
When Adam and Eve were in the Garden, they had the opportunity for eternal life, but when they disobeyed God by taking of the tree of the knowledge of good and evil, they did what was right in their own eyes, and mankind has been doing that ever since and we’ve seen how that turned out. It’s never good to do what we think is right in our own minds because it’s outside of the Word of God (Judges 21:25), and with that in mind, it was “when the woman saw that the tree was good for food, and that it was a delight to the eyes, and that the tree was to be desired to make one wise, she took of its fruit and ate, and she also gave some to her husband who was with her, and he ate” (Gen 3:6). We can’t blame Eve…Adam was standing right there with her when she took it. He did nothing to stop her, and as her husband, he is more culpable than she is, although surely both are guilty. God had already told them, “but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die” (Gen 2:17), and even though they didn’t die instantly, they had died spiritually, and now the physical life they currently had would end someday, and so it was “because of one man’s trespass, death reigned through that one man, much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ” (Rom 5:17), however believers can thank God that, “as by a man came death, by a man has come also the resurrection of the dead” (1st Cor 15:21), and that Man is Jesus Christ.
Did they Repent?
There is no real evidence that they ever confessed their sin to God and that they repented of their actions. Eve blamed the serpent, Adam blamed his wife (and ultimately, God Who created her), but neither seemed to accept responsibility for their disobedience. Although repentance is a God-given ability (2nd Tim 2:25), there is little evidence that they did, but that’s an argument from silence. We could say, neither did they do such and such, so just because the Bible is silent on their repenting, it doesn’t mean they didn’t. God Himself provided a sacrifice for them when He killed some animals in order to provide them with clothing, so God made the first sacrifice, oddly enough, for mankind, and not the other way around, but does that mean their sins were covered by the shed blood of an animal? We know that animal blood itself only covered sins in the Old Testament, never really taking them away (Heb 10:4). Only Jesus’ shed blood can take away our sins, so just because God sacrificed animals to provide them with a covering, this doesn’t mean they were saved. I can certainly see how some Bible scholars see God providing them with a “covering” of animal skins, but it’s rarely mentioned again after this. It may be the first animal sacrifice ever, and the only one where God sacrificed for mankind, but later, God would do this again, by sacrificing His One and only Son, Jesus Christ (John 3:16). Those who trust in Him do not have to wonder about their own security in Christ. After the fall, Eve does seem to exhibit at least some faith in God when she says, “I have gotten a man with the help of the Lord” (Gen 4:1b), meaning the birth of Cain. We know how Cain turned out, killing his righteous brother Abel, so did Adam and Eve  repent? What is also missing after the fall are Scriptures that say God continued to walk with Adam and Eve. Prior to the fall, Adam and Eve had a close, personal relationship with God, as they “walked with God.” This type of language usually signifies a close relationship with God, also having close fellowship, but there is nothing more ever said about their walking with God again, and God basically ceases to communicate with them like He did in the Garden.
Adam; Symbolic of Sin
So many times the Scriptures refer to Adam as man, the sinner. In the New Testament, Adam has several references which associate him with sin (see, 1st Cor 15). After Cain murdered his brother Abel, Eve gave birth to another son, names Seth, which means “appointed,” so Eve believed Seth was appointed by God, but does that mean appointed to be their Savior? Again, Eve gives credit to God, saying, “God has appointed for me another offspring instead of Abel, for Cain killed him” (Gen 4:25). This again expresses a bit of faith in God and in His sovereignty. Perhaps she was still hoping for an “appointed” one, or a Redeemer to be born. Did God tell them that in time, they would have a Redeemer? It seems so in what is the first mention of the gospel (Gen 3:15). In time, God would crush Satan’s head, even though Satan would bruise His heal (Gen 3:15), and that would happen at Calvary. So what’s missing in all these accounts of Eve’s faith in God? Adam! What does he have to say about faith in God? After the fall, there is a roaring silence from Adam about God, so some believe Adam was not saved but Eve was. We know Adam represented the federal head of humanity, but he failed in is mission to even lead his wife properly, but where Adam failed, Jesus Christ triumphed. By Adam’s attempt to clothe himself with leaves, perhaps he was trying to cover his own sins and provide his own covering, which of course God will not accept (Eph 2:8-9). Some people still believe they can cover themselves, but that’s a dangerous error to fall into, because the Bible says, not one of us are good (Rom 3:10), and none can do any good (Rom 3:12) that God will accept. All of us (including me!) fall infinitely short of God’s glory, but that’s exactly why grace is so very amazing.
Some believe Adam and Eve were both saved. Some that only Eve was, and others believe neither of them were, so here’s what I can be sure of; we don’t know for sure, so I am not sure we can know with absolute certainty whether Adam and Eve were saved. There is a bit more compelling evidence that Eve might have been because she is still expressing faith in God during her childbearing, but this too is not 100% proof that Eve was saved. I’m not sure we can reach a conclusion either way since the Bible does not give enough precise information on whether the two were saved, whether only one of them were saved, or whether neither of them were saved. We will know someday on the day we enter the kingdom, so unless you have been brought to repentance and faith in Christ, you may never know since you will be shut out of the kingdom, but of course, there is no reason you can’t believe. Let Jesus speak to your heart  right now, believers and non-believers alike; “I am the resurrection and the life. Whoever believes in me, though he die, yet shall he live, and everyone who lives and believes in me shall never die. Do you believe this” (John 11:25-26)? That is the question for the ages…”Do you believe this?”
Read more related to this topic here: Why Did Cain Kill his Brother Abel? 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible: English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.