1 Timothy 2:14 NIV
[14] And Adam was not the one deceived; it was the woman who was deceived and became a sinner.
Right. You become a sinner when you give in to temptation. Being tempted is not a sin. Jesus was tempted, but did not sin. Giving into temptation is sin. So technically the first person who sinned was Eve, but Eve was under Adam's authority as his wife, and therefore Adam was responsible. Adam also ate with her, so Adam was responsible personally as well as responsible as a leader.
You can just read the Bible and see that sin was in the world before the fall.
But like I said before, sin was not counted where there was no law. Adam represents all of us. We all sin because he sinned. Sin came through him into the world, that is, to mankind.
But before Adams transgression, sin was present. Eve sinned. Satan sinned...
And Adams grandma would have sinned too.
I think you are confusing terms a little bit. Let's define these words. Oxford languages:
evil - profoundly immoral and wicked
temptation - the desire to do something wrong or unwise
sin - an immoral act considered to be a transgression against divine law
soul - the spiritual or immaterial part of a human being or animal, regarded as immortal
So Satan was evil. Evil existed in the spiritual realm but Adam and Eve did not know it. They knew about it because of the tree, but they did not know it intimately. They knew good intimately, because they knew God intimately, but they did not know evil.
Agree?
Then God gives a commandment - do not eat the fruit of the knowledge of good and evil. As in do not learn how to be evil.
Eve is tempted - being tempted is not a sin. Eve gives into temptation, eats the fruit, and simultaneously sins and learns how to sin or learns what evil is and how to be evil. Adam does the same.
Agree?
So yes, technically Eve sinned first, but she was Adam's flesh and bone and she was under Adam's authority as his wife, so what she did Adam did. Adam is being held responsible for bringing sin into the world not only because he ate, but also because of his status as being Eve's husband. Just like the pastor of a church would be held responsible if the church decided to burn a witch, for example.
Ok, so Adam and Eve sin/learn how to be evil, and experience spiritual death - a separation from God. And that is the fate of every human being that has ever lived, we are spiritually dead and separated from God. We get to the judgement day, and God's like well, you're separated from Me, so no heaven for you. Except that God didn't want that. So He made a plan. Spiritual sin could be passed onto a physical body of a lamb, and the lamb could die a physical death, but the person would no longer have that particular sin, so the person would be made spiritually alive. Except that that only worked for one sin at a time. So He sent His own Son, who took a physical body of a human and died both a physical and a spiritual death in exchange for all of our sins at once, and that's how we can be raised both physically and spiritually to an eternal physical and spiritual life.
Agree?
And God also said that for those people who lived between Adam and Jesus there was an slightly modified path - all they had to do was believe in God, and it would be credited to them as righteousness because their sins would get paid for by Jesus anyway.
So far so good?
Ok. Now let's introduce Adam's grandma. Let's call her Lucy. Lucy is a person, with a soul because, like you say, a person is a person is a person. She lives without knowing God because, as you say, God had not had a relationship with humans. She also does not know how to be evil and she does not sin. She does not sin because there is no law. She does not know how to be evil, because Adam would have known it and he didn't. She dies. Adam and Eve sin. Dead Lucy who never disobeyed God and did not know how to be evil is now considered sinful because "all have sinned". By now she is dead, so she can't decide to believe in God. At judgement day, where does she go?
PS. This, by the way, has nothing to do with whether evolution is real. This has to do with whether God chose to create humans by evolution, or if God chose to just create them and give them a body of a mammal, but we don't know how exactly. What we are trying to do is see if we can use theology and logic to discover whether Lucy could have been Adam's ancestor.