Why did Allah Almighty create Adam to be His vicegerent on Earth, then came the story of the tree and the temptation?

There is no contradiction between God's decree to create Adam for the vicegerency of the Earth and the story of the tree, for the latter was a direct cause for the fulfillment of the former decree. The incident of eating from the tree holds great wisdoms, among them: the beginning of human accountability (takleef), the recognition of Satan as a true enemy to them, and the establishment of the concept of repentance. Adam's expulsion was not a punishment but rather the realization of the eternal wisdom in spreading his progeny and entrusting them with responsibilities and testing them on Earth.