What is the biblical evidence against the idea that God, pre-Fall, always intended Jesus' crucifixion? The "tree of the knowledge of good and evil" which God placed in the Garden of Eden (Genesis 2:17) has long been acknowledged by Christians as a symbol of humanity's free will. Having placed this here, it seems God could have always been aware of a (perhaps) inevitable progression of sin and a consequent need for redemption. From Acts 2:23, 1 Peter 1:20, and The Hero's Journey, for example, I've concluded that God had always known that Jesus would be crucified.

New personal evidence from "The Star of Bethlehem" (2012): the constellations align with remarkable symbolism around the time of Jesus' conception, birth, and death, indicating intention of divine timing in concert with the cosmos (Psalm 19:1-4). *spoiler alert* In order for such clock-work-type timing, "That means that from the very moment that God flung the universe into existence, He had to know exactly when he would enter the human race as a man and when the Messiah would expire on the cross.".

My edited question is this: what groups believe that Christ's sacrifice (or Israel's long history, for that matter) was never part of God's original plan for humanity, and what do they claim as the biblical basis for that idea?
This is a Bible based answer. This is what Jehovah's Witnesses believe, so it is how they interpret these scriptures. Since you asked for a Biblical basis, not the beliefs of Jehovah's Witnesses, the reasoning behind this interpretation is also included in this answer.

Got created Adam and Eve to be good, not bad. So there was no wickedness within them at the time of their creation, otherwise that would mean God intentionally put wickedness inside them. That would be contrary to the principal at James 1:13 "When under trial, let no one say: “I am being tried by God.” For with evil things God cannot be tried, nor does he himself try anyone."

The placement and name of the tree of knowledge of good and bad, along with the command not to eat from it does not suggest God already knew they would choose a path of sin. Instead it suggests he knew they would need to decide for themselves if they would accept his sovereignty or not, that they were capable of choosing either path, and that this was a critical issue facing humanity. This was not an unreasonable command. It is not like he made them starve and then placed a tree in front of them and told them not to eat from it. In preface to this command, he said "From every tree of the garden you may eat to satisfaction." (Genesis 2:16). He was not trying to trick them into going down a path of sin and death. The idea was to have them decide if they appreciated their heavenly father and all he had done for them, and express this appreciation through loving obedience, or if they would selfishly reject his authority. The choice was theirs to make, but he still did many things to nudge them toward choosing to obey him, which was the loving thing to do. For example, he gave them the life they had. God even created Eve as a wonderful companion for Adam, and Adam was so happy with this that he waxed poetic (Genesis 2:23). God placed them in a beautiful garden and gave them meaningful, fulfilling work to do (naming the animals, taking care of the earth, and filling the earth with their offspring) (Genesis 2:19, 20; Genesis 2:15; Genesis 1:28). Consider all God gave them prior to having them make a choice. Also consider his words at Deuteronomy 30:19 where God is pleading with the Israelites to choose life.

If Adam and Eve had chosen a path of obedience they would have produced perfect offspring, not sinful ones (Romans 5:12). It was only after mankind's fall into sin that the first prophecy involving Jesus' sacrifice came about, at Genesis 3:15. This does not mean God already planned for things to play out that way. It just means that man's actions, or anyone else's for that matter, cannot prevent God's purpose from being fulfilled (Isaiah 55:10, 11). Immediately after mankind's sin seemed to threaten God's original purpose for the earth to be a home for humanity, filled with perfect, happy people that live forever, he set things in motion to rectify the situation, and assured us of the outcome (Genesis 3:15).

It is true that details about Jesus' birth, ministry, and death were foretold in the scriptures. But this does not mean those details were already known prior to mankind's fall into sin. Whatever God does or does not choose to foresee, and whatever implications it may or may not have about our free will and the paths we choose, we can say he does have control over his ability to see into the future, as opposed to this being an out of control ability. Free will is a gift he has given us, and he makes sure to use his abilities in a way that does not infringe upon this gift. Our choices would be meaningless without that gift.

For more detailed information see this, which also explains a different interpretation of 1 Peter 1:20 than what might more readily come into a reader's mind. However, explaining that scripture gets into a whole other branch of our beliefs that is outside the scope of this topic.

References:

https://www.jw.org/en/publications/books/draw-close/wisdom/divine-wisdom-jehovah-god/
https://www.jw.org/en/bible-teachings/questions/free-will-in-the-bible/
https://www.jw.org/en/publications/books/bible-study/gods-promises-for-humans/