Does God require us to have faith because Adam and Eve sinned?

The argument,

Given that faith requires an obedient, seeking heart, it almost seems like this is a way to remedy the fall of humankind, and to restore our obedience to God.

It is true that faith is a requirement to please God.

And without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him. (Hebrews 11:6, NIV)

But it is not true that God demanded faith only after the fall of Adam and Eve.

And the Lord God commanded the man, “You are free to eat from any tree in the garden; but you must not eat from the tree of the knowledge of good and evil, for when you eat from it you will certainly die.” (Genesis 2:16-17, NIV)

The first command given by God was not to eat the fruit from the tree of knowledge. God gave a warning to Adam "when you eat from it you will certainly die". Here God was not only giving a command but demanded trust from Adam. It is like saying "Believe me Adam when I say 'you will certainly die'". Here death was not yet experienced by Adam but I believe that it was well understood by Adam. Allow me to even make a conjecture here that Adam understood the consequence of death that it was separation from God and probably, going to Hell. Here Adam had to have faith in God and the same goes to Eve. I believe that Adam explained very well about the fruit and the punishment to Eve but she failed to have faith in God and believed the words of the serpent who was inferior to her. In other words, Eve had no faith. She was not even putting her faith on the serpent. To put faith on the serpent would mean that even if death actually came over them, the serpent could nullify it's effect. But the serpent did not promise anything to Eve but only said that she will become like God. Eve did not ask the serpent, "OK, if what God said was true, do you have the power to save me from death?". Eve was only curious about what the serpent was saying and wanted to try it, probably, without a second thought. Because Eve failed to have faith, she transgressed, which Adam followed because he loved his wife and now we are all doomed.

Faith was always a requirement from the beginning. Now that Jesus opened the way to God, it is still faith alone that can lead us to God. Without having faith that Jesus is the way to heaven, how can anyone please God. Without believing that Jesus is the Son of God, how can anyone please God who sent Him? If Eve had faith in God, we would not have suffered and Jesus should not have died. Now that Jesus died for us, we need to have faith in Jesus to reconcile with God again.

Jesus said,

“Very truly I tell you, whoever hears my word and believes him who sent me has eternal life and will not be judged but has crossed over from death to life. (John 5:24, NIV)

I could be wrong, but it seems that people are confusing obedience and faith as terms. For me, faith and obedience are two separate parts of a relationship with God. Obedience is following what we beleive God is asking us to do. Faith is believing that God exists, even though he operates within our lives in a non-scientifically provable fashion. As I see it, Adam and Eve never needed faith since they had a direct physical relationship with God. Faith was not needed to walk and talk with God in the garden, it was happening right in front of Adam and Eve's eyes.

Slight tangent here: Obedience or faith, which is more important to God? For some weird reason faith seems more important to God than obedience. I say weird because most sins cause harm to other people. Murder, theft, lying, adultery add pain and suffering to the lives of those around us. Faithless-ness on the other hand is either victimless or hinders just one person's spiritual development. It seems that disobedience should be considered more toxic than faithless-ness. Clearly God tolerates disobedience since he is willing to forgive every sin, with the exception of faithless-ness. Faith or lack thereof seems to be the main block from being saved. John 3:16 does not say "Even those who don't believe in Jesus will have eternal life".

Let's use an analogy to emphasize this point. Imagine if suddenly every person in the world converted to Christianity. But each person simultaneously committed ten more sins on average each day. What would be the result? This would be a boon to Christianity, with about 6 billion new believers. But global sinfulness overall would have gone up too. In this scenario, Christianity is still better than ever.

Now imagine the opposite. Imagine if every person on Earth lost faith in Christianity. But each person simultaneously committed ten LESS sins on average each day. What would then be the result? Even though, globally sin is reduced, this is disastrous for Christianity, zero practitioners. In four generations nobody would even be alive anymore to remember it as a religion. Christianity becomes extinct.

This analogy shows that disobedience does not by itself destroy a religion, however a lack of faith kills religion.

This is why God / religion seems to tolerate disobedience more than faithless-ness.

This is just my observation, any thoughts?

This is a direct answer to the question in your title.

The bible states that all are required to have faith (need salvation) not only because of Adam's sin, but because "all sinned."

"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." (Romans 5:12)

Original sin began with Lucifer, the “I will” sin. Isaiah 14:13,14 “For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north: I will ascend above the heights of the clouds; I will be like the most High.”

Eve was deceived and placed her faith in the words of the serpent rather than in the Word of God (transgressed faith ). Mary, in contrast, placed her faith in the Word of God and said: “Let it be as you say”.

Adam sided with Eve, “her will” rather than God’s will. In contrast, the second Adam, Jesus Christ said “thy will be done” and bore the sins of mankind, resulting in grace being eternally extended to mankind, grace which is apprehended by faith.

The original sin is born from a “self-sovereign" perspective, "My will be done. Do not impose your will upon my life." Contrast: “Thy will be done on Earth as it is in Heaven."

God’s grace is tangible evidence that we should want God’s will to be done in our life. So where does “me-centeredness" come from? Originally, Lucifer transmitted to Eve by deception, who then transmitted to Adam by fear, or faithlessness.

Transgressed faith was the window in which man fell out of a relationship with God. It stands to reason that man must enter into a relationship through that same window of faith. After all, we are saved by God’s grace through faith.