God said that every person is responsible for their own sins.
We cannot be blamed for other people's sins.
We are not responsible,and are not blamed,for the sin of Adam and Eve,nor is their sin applied to us in the way of them eating of the tree.
But it is applied to us in a different way.
Adam and Eve were created knowing God,and they would of never sinned if an outside source did not tempt them,and when Satan first tempted Eve,she said plainly we may not eat of the tree,so Satan tried a different approach and appealed to her ego,that she could be greater than what God created her to be,and she ate of the fruit.
God gave Adam and Eve a choice,so that is why the tree of the knowledge of good and evil was in the garden.
They would of never sinned if an outside source did not tempt them,so God allowed Satan to tempt Eve,and she ate of the fruit,and sinned,and then Eve was the outside source that tempted Adam by showing him that it was alright to eat of the fruit,for she did not die,and Adam ate of the fruit,and sinned.
Their sin is their sin,and our sin nature cannot apply to us by their sin of eating the fruit,but it is still a result of why we have a sin nature.
It is the tree of the knowledge of good and evil,and no longer would Adam and Eve not know any choice but to follow God,but now they would have a choice between good and evil,and would have to make the choice to follow God instead of always following God like they did before Satan tempted Eve.
So all of Adam and Eve's offspring,which Eve is the mother of all that is living,is born with a choice between good and evil,and are born not knowing God,and will do evil before they accept God,so all are born sinners,and fall short of the glory of God.
But concerning babies,and children not at the age of accountability,their angels always behold the face of the Father for the little ones,so although we are born in to sin,we are innocent until we know right from wrong correctly,but we will sin before we accept God properly.