I think this is wrong, but these are my own thoughts and may be wrong, too.
Adam and Eve were not born with Original Sin, as their actual sin was was started Original Sin.
AFAIK, they were also free from concupicence, which I believe is more than just “the tendency to sin”. Concupicence may be a result of Original Sin, not the cause. The sin of Adam and Eve removed from them the Sanctifying Grace which God had blessed them with from birth. Because of that sin, all their descendants were not able to receive that Grace through propagation, as God had initially desired. Lost, also, was the freedom from concupiscence that God had blessed them with. Concupiscence is defined by the Catholic Encyclopedia as:
We can see from the Genesis account that a change came in Adam and Eve after the Fall – namely, their desire to hide themselves because they were naked. So although the sexual appetite is probably the most powerful of the lower appetites, Adam and Eve did not seem influenced by it until after the fall. It can be concluded, then, that they were free of concupiscence prior to the fall, but not afterwards. Since it appears to be an aspect of human nature (even Jesus was tempted by Satan using food - a base appetite), I think God must have specifically given Adam and Eve the gift of freedom from concupiscence, which they lost when they fell from Grace.
I’m certainly willing to entertain others’ thoughts on this, though. I am no expert…
Peace,
javelin