Can the ancestral sin doctrine (and Paul's epistles) survive without a single breeding pair?

I'll answer a tangential, but implied question: Can Pauline doctrine survive "physical death before Adam?"

Answer: yes, from an Old Earth Creationist perspective.

Romans 5:12 Therefore, just as sin entered the world through one man, and death through sin, and in this way death came to all people, because all sinned

The Bible states that the doctrine of sin rests on that story of one man, as you observed.

Gen 2:17 but of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

The literal historical figure of Adam literally died in the day he ate the fruit.

If you take a Young Earth Creationist view, his body's cells started to decay. If you take an Old Earth Creationist viewpoint, he spiritually died and became in need of a Saviour at that instant. In this latter view, there is no conflict with animals eating each other (Triceratops with T-Rex-tooth holes in their frill predating man, for example) and our need for salvation from our sins.

(Firstly, this site is NOT a place for searching the TRUTH)

Can the ancestral sin doctrine (and Paul's epistles) survive without a single breeding pair?

Answer: NO

If we reject the Biblical story that humanity started from a single pair, the whole christian concept of Sin and Salvation is meaningless. If evolution is true and that humanity started from multiple couples, then the "original sin" concept may not apply to all mankind. Some will born with sin and some without, which infers that Jesus did not have to die for all of mankind but only for those who are born from sinful parents.

Can we find anyone without sin?

Answer: I don't think so.

It won't be an easy thing to find a person who can boastfully say that he/she is without sin. Many times we fool ourselves into thinking that we are good enough but I say it is only due to our self righteousness nature. We never see other's fault but when we erred, we make excuses. Believe it when the Bible says "No one is perfect". Jesus even once proved this to the Jewish religious leaders that no one is righteous.

John 8:1-11 (NKJV) -Excerpt

Then the scribes and Pharisees brought to Him a woman caught in adultery. And when they had set her in the midst, they said to Him, “Teacher, this woman was caught in adultery, in the very act. Now Moses, in the law, commanded us that such should be stoned. But what do You say?” So when they continued asking Him, He raised Himself up and said to them, “He who is without sin among you, let him throw a stone at her first.” Then those who heard it, being convicted by their conscience, went out one by one, beginning with the oldest even to the last. And Jesus was left alone, and the woman standing in the midst. When Jesus had raised Himself up and saw no one but the woman, He said to her, “Woman, where are those accusers of yours? Has no one condemned you?” She said, “No one, Lord.” And Jesus said to her, “Neither do I condemn you; go and sin no more.”

If we agree to the fact that no one is exempted from sinning, then we can make a clear deduction that Bible is true and that Adam and Eve were the first couple by which, through their disobedience the whole humanity is under the power of SIN.

Allow me to rephrase the question in terms more suitable to the internet...

Whether God requires His creatures to have sex in order to condemn themselves?

Objection 1. It would seem that God does not desire His creatures to continually create themselves bearing the fruits of original sin, but is in fact happier with those whom he deigned to create or beget without sin. When God created Adam and Eve, sinless originally, He said that they were good (Gn 1:31). When God sent His messenger to Mary, sinless as she was, he said she had found favor with God (Lk 1:30). When God the Father spoke to His Beloved Son (also sinless) He said that in Him He was pleased (Mt 3:17).

Objection 2. Furthermore, God must need our participation to perpetuate Original Sin. Because without His creatures copulation, there would be no more Original Sin for Baptism to wipe away the effects of, thereby negating a vital sacrament of initiation.

Objection 3. It would seem that our nature inherits Original Sin because our nature comes from our parents. Since science might (today at least) have us believe that we had no tangible first human parents as evinced in the Bible by the persons of Adam and Eve, there could not have been two such parents to fall for us to inherit Original Sin from. Therefore cloned human beings would not be subject to the effects of Original Sin, nor would those who were not of the branch of Adam and Eve (let alone Noah).

On the contrary, Original Sin is a mark on the immortal Human Soul, created by God, for God and only from the Love of God. It is not sex that imposes concupiscence. So, No God does not require humanity's participation (though carnal unions or sterile cloning) to impose Original Sin on it. And yes, Original Sin will survive (thrive even) in a Brave New World. As Uncle Chestnut says:

Certain new theologians dispute original sin, which is the only part of Christian theology which can really be proved.

GCK - Orthodoxy

His proof for Original Sin, although tongue-in-cheek, will exist where ever humanity exists.

I answer that, this entire question could be swept away by the common Catholic teaching that the first 11 or so books of Genesis may be primarily useful in senses other than the literal

the first eleven chapters of Genesis, although properly speaking not conforming to the historical method used by the best Greek and Latin writers or by competent authors of our time, do nevertheless pertain to history in a true sense, which however must be further studied and determined by exegetes;

the same chapters, in simple and metaphorical language adapted to the mentality of a people but little cultured, both state the principal truths which are fundamental for our salvation, and also give a popular description of the origin of the human race and the chosen people. If, however, the ancient sacred writers have taken anything from popular narrations (and this may be conceded), it must never be forgotten that they did so with the help of divine inspiration, through which they were rendered immune from any error in selecting and evaluating those documents.

Pope Pius XII Humani Generis - 38

Pope Pius XII can concede nothing on the Spiritual and Everlasting Truths found in the first chapters of Genesis.

Reply to Objection 1 Although it can add nothing to His greatness, God is pleased by every one of our selfless acts of love and kindness. Otherwise He would not have said Blessed are they who... (Mt 5:1-12) Even though we suffer the residual effect of Original Sin (i.e. we have an inclination to sin) it can be overcame with the Divine Help.

Reply to Objection 2 Although St. Paul says that where sin abounds, grace abounds all the more. and during the Exsultet on Easter Vigil it is proclaimed "O happy fault, O necessary sin of Adam, which gained for us so great a Redeemer". It is clearly not good that we are borne into concupiscence and that is why Jesus is coming again one day. When we're borne into eternal life, we will be freed from that sinful inclination even though our souls were created and imbued with it. The Ox says:

Original sin is caused by the s*m*n as instrumental cause. Now there is no need for anything to be more in the instrumental cause than in the effect; but only in the principal cause: and, in this way, original sin was in Adam more fully, since in him it had the nature of actual sin.

Summa Theologica Q.83 A.1 Reply to Objection 2

So, Adam had original sin, but it wasn't passed to him through his parent's sexual intercourse.

Reply to Objection 3 Although it is not clear whether anything besides children of Adam have human souls. Science has not the competence to trounce theology on the topic of human evolution (Youcat 42) Nor should theology inform scientific theory. The key point is:

Souls are not inherited Each is a distinct creation of God and is united with the body at the time of conception.
This is the faith - Canon Francis Ripley

There is nothing in science that can contradict this supernatural truth for this and many other reasons Pope Pius XII says

For the faithful cannot embrace that opinion which maintains that either after Adam there existed on this earth true men who did not take their origin through natural generation from him as from the first parent of all, or that Adam represents a certain number of first parents. Now it is in no way apparent how such an opinion can be reconciled with that which the sources of revealed truth and the documents of the Teaching Authority of the Church propose with regard to original sin, which proceeds from a sin actually committed by an individual Adam and which, through generation, is passed on to all and is in everyone as his own.

Humani Generis 37

Human nature is not strictly speaking a property of the human soul, the Rational Immortal Soul is God's gift to human nature. Aquinas and Aristotle teach that everything has a nature and a soul. But the powers of the human soul vary considerably with those of the rocks and fishes but the danger is that they can suffer the effects of Original Sin and even if there were no women left on earth, each cloned man would still be limited by whatever God determined the powers of his soul would be imbued with. In this case one needs to interpret literal inheritance or can posit a sideways inheritance in Paul's writings. But in the absence of a test for a soul in those who we hope would be naturally having one, it is impossible for science to know whether cloned individuals would likewise have or not have a soul.

Can the ancestral sin doctrine (and Paul's epistles) survive without a single breeding pair?

Answer: YES

When Adam fell and sin was ushered in

"the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope 21thath the creation itself will be liberated from its bondage to decay and brought into the freedom and glory of the children of God." (Romans 8:20)

In other words, God put all of Creation under the curse, not just Adam. One need only remember that the ground was cursed because of Adam, and the animals were cursed because of Adam - even though only Adam sinned.

Animals share no DNA*, no gametes, nothing that could have been inherited from man. And yet, they were subject to futility. As such, this discredits the idea that sin is a disease or a genetic mutation passed from one generation to the next.

^{*I understand that animals and humans do actually share a common codebase of DNA, and that chimpanzees use 99% of the same genetic code. I am using this is the common parlance idea of 'passing down DNA from one creature to the next,' not in the biological common code sense.}

As such, one can still assert fully as Paul does in Romans 5 that

"Therefore, just as sin entered the world through one man, and death through sin, and in this way death came to all people, because all sinned—

To be sure, sin was in the world before the law was given, but sin is not charged against anyone’s account where there is no law. Nevertheless, death reigned from the time of Adam to the time of Moses, even over those who did not sin by breaking a command, as did Adam, who is a pattern of the one to come.

In other words, it is not that sin entered with the Fall, but rather the Law. All of Creation became subject to the law of futility and death.

Does it seem unfair? That is outside of the scope of the question. Rather, it should be understood that even if there was a "Lillith" who wasn't part of the apple incident (and yes, I know the Bible doesn't say apple!), it would be irrelevant. It is irrelevant because it isn't sin that entered, but the law.

And everybody was subject to that.

Preface that this isn't a site for debating what is true, it's merely for learning what s taught/believed within Christianity. See How we are different than other sites?

With that in mind, most of your question is off-topic, but I believe that the core concept from your question can be addressed if we phrase it as follows:

Do any Christian groups believe that without a literal Adam, the concept of original sin has no meaning?

I'm going to answer that portion, in the interest of answering the heart of the question, filtering out the portions that are off-topic and/or controversial/disputed within Christian circles.

The short answer is tat yes, some Christians, namely Young-Earth Creationists teach and believe exactly that. Ken Ham, Kent Hovind and other well-known YEC proponents teach exactly that.

One such example from CCEL

Is it important:

Well, if there was no first Adam, could there also not be a second Adam, our LORD Jesus Christ? For as in Adam all die, even so in Christ shall all be made alive...it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit." 1 Corinthians 15

If death did not come as result of Adam's sin, then why did we need a savior to deliver us from death unto life? "Just as sin entered the world through one man (Adam), and death through sin, and in this way death came to all men, because all sinned"- Romans 5

Was Jesus' real if his geneaology account is not trustworthy? Jesus was the son of Joseph, who was the son of ..., the son of Seth, the son of Adam (Luke 3) - Can the Word of God be trusted for its specific geneaology or is it mythology?

I also posted on the subject at Why do Young-Earth Creationists make such a big deal about the YEC view.

Not all Christians see it thus way, of course. This represents only one view within Christianity.