We don't know why humanity was banned, Lucifer corrupted Lilith not Adam and Eve. Chuck being an unreliable narrator, the Garden restoring Jack's soul doesn't prove that he was lying or being truthful in his statement.
When [[God]] created the world, He created the Garden of Eden as a crossroads between humanity and divinity, where he kept His prize creations Adam and Eve. However,
when [[Gadreel]] allowed [[Lucifer]] to enter the Garden and corrupt Adam and Eve, they were banished from the Garden along with the rest of humanity. The Garden of Eden was hidden away and appears to exist in an alternate realm outside reality. The Garden can be accessed if a non-human entity consumes [[the Occultum]]. According to [[Castiel]], the Garden is "the crossroads of divinity and humanity" and no one has been there since the exile of humanity.
Within the Garden is a young girl and an albino python snake. The young girl appears to have great knowledge of the Garden, but her actual purpose is not known. The snake or the nature of the Garden itself appears to have the ability to restore
lost [[souls]] in [[soulless]] people.