Well, let me preface this by saying I am not a theist, I don't take the bible literally, so that includes a literal understanding of A&E and the sin brought into the world by their specific action. Also, I believe in the theory of evolution and do not believe we were created perfect and then fell. Nor do I believe we are 'separate' from God, theistically understood (ala A&E and sin) or that in the same vein, we need saving from sin - again understood theistically - which, to me, it seems, you are referring. Let me add, I am (non formal religious) Christian, believe “God”Is (again not a supreme being in his heaven, judging actions and keeping score, etc.,) and, to your point, I believe we can speak intelligibly about ‘sin.’
Some contemporary theologians use the conception of the Greek Fathers, such as Irenaeus (200 years before Augustine), concerning the gradual movement of the human being from an 'initial site of immaturity" which contrasts with Augustine's fall from the original state of righteousness (perfection). So, there were different views early on. Sadly, the Western, Roman expression and Augustine prevailed.
Many define sin as self-centeredness or selfishness (also depicted in the Eden story) and further that the original, actually the only sin is self-centeredness. And it shows itself in numerous ways: simply, I lie for me, I lust for me, I kill for me, I dishonor another for me, I am envious of another for me and on and on. And, it seems evident that selfishness is the act of man and so it can be said that selfishness ‘enters’the world when 'man' steps forward in the process of evolution (which could dovetail with ‘possibility’stake). Now, Spong, among others, notes that early man, of necessity was self-centered: it was survival and he had to look out for and protect #1. Makes sense! However, as man progressed, it can be asked if the circumstances have changed and looking out for # 1 has taken on a life beyond survival (difficult subjects include slavery, colonization, western expansion, re-settling native populations, Nazism, Henry VIII, Trump, or simply Cain and Abel). Others speak of individual and communal self-centeredness (both are witnessed in the examples cited) that all newborns are born into.
Leaving religion to the side for a moment, there is something to the idea that we are born into self-centeredness: it ‘marks' all men and women. And, at its worst, it destroys life, community and is devoid of ‘humanity.’There seems to be an awareness of this reality: of a killer, a terrorist, or someone who rapes a child, we say, "what a monster" or "he's inhuman" or she is an animal”or "he is evil incarnate." And of the cop or fireman on 911 or a soldier who saved his buddy, a woman who dies giving birth, knowing the risk, we often hear: "the finest human being I've ever known" or “the best of us”or “what an incredible person" or "this guy is someone to live up to." The truly self-centered, the most selfish among us, who care nothing for others, we strip of humanity (the monster) and those who give to others, who have concern for others, the most loving among us, we heap humanity on then (the best of us).
One definition of sin is 'missing the mark' and the mark is to become (truly) human, understood/defined as self-less, compassionate or loving. And to the degree we are selfish, to that degree we miss the mark, we 'fail' to (self-) actualize, we fail to become (truly) human. Obviously, the term human here connotes more than species.
So, can self-centeredness be called sin? From the Christian perspective, the answer is yes! And if we talk of being saved from sin, we start with Baptism: properly understood, is an orientation away from self-centered behavior and toward self-less-ness. There is no magic washing of sin; it is symbol and the human community (parents, godparents, community) is the essential element in the nurturing of a child away from self-centeredness and toward selflessness (compassionate concern or, apologies, love). This locus of love is essential for a truly human life.
Is sin separation from God? Well, self-centeredness or sin is seen as separation from the possibility of our best self: we are off the mark. Then, before we get to God, the question is how can this separation be overcome? Simple, as shown, by becoming less and less selfish - or to put it in a positive light: by becoming more and more self-less, by becoming more loving.
Finally, Christianity believes that God is Love. So, are we separated from God and is God necessary for salvation; do we need to be saved? If God is Love and if love or loving is what enables us to be truly human, then until we love, it could be said that self-centeredness is the textbook opposite of and separation from love. From the Christian perspective, self-centeredness (sin) is separation from love (God). It can be said we need to be saved from sin, which, in this scenario simply means, we need to be healed of selfishness, and, thereby, made whole, i.e. human. What is a whole human being? The fireman on 911, the mother who gives here all on a daily basis, the man who tries to be compassionate and concerned for those in his life, even the stranger, the kid who decides not to be a bully: all are on the way to wholeness (in the Christian understanding). BTW, it is not a consistent process and sometimes we simply do a lousy job of being human: two steps forward, one back, one step forward, four back and on and on.
So, is God necessary for salvation? To become whole or human, one becomes selfless, one loves (and, thereby, selfishness, the only sin, is overcome). One must 'embody' love, one must 'become love;' one must allow love to become flesh, which simply means to reside, to be expressed in their flesh, in their lives. This is the 'incarnation' of Love; this is the incarnation of God. Man cannot be human without love; man cannot be human without God. God/Love is necessary for man to be whole (i.e. salvation although I actually never use this terminology anymore because it gets in the way, given its historical baggage).
In Christianity, even if there were no sin, God would still be one with man (and this too is captured in the story of Eden). The Lover always wants to be one with the Beloved: even when man was not ‘separated’from God in Eden, God is with/for man: it is what love is; it is what love does.
I always thought the very best reason to have a child is simply love. It is pure gift, so another, yet to be, might be and have life. We, hopefully, or the best of humanity, do not create life so it worships us, to obey us, to be a little us, so we can bask in our glory; we love, we create so the beloved may have life and the desire is always to be with/for the beloved as it moves to and lives fully. In the Christian perspective, properly understood, this is the reason for creation. It is Letting Be (which is God).
Please note, you asked for a Christian explanation and what I have tried to do is give you an explanation based on a more contemporary take on Christianity.