Why did Allah create us?

A helpful way to answer this is to separate What is our purpose? from "Why did Allah choose to create at all?" Allah tells us our purpose: "I did not create jinn and humans except to worship Me." (Qur'an 51:56). But if the question is, "Why did Allah will for there to be a creation in the first place?" then ultimately, Allah creates because He wills and chooses to create. His will is not subject to a higher authority or a need for justification. Allah says: لَا يُسْأَلُ عَمَّا يَفْعَلُ وَهُمْ يُسْأَلُونَ "He is not questioned about what He does, but they will be questioned." (Qur'an 21:23) And Allah says: وَرَبُّكَ يَخْلُقُ مَا يَشَاءُ وَيَخْتَارُ "Your Lord creates whatever He wills and chooses." (Qur'an 28:68) So Allah did not create us because He was lonely, incomplete, bored, or because He needed worshippers. Allah is Al-Ghaniyy completely Self-Sufficient. Even if nothing existed besides Allah, His perfection would not decrease in the slightest. At the same time, Allah has perfect Names and Attributes: Al-Khaliq (The Creator), Ar-Rahman (The Most Merciful), Al-Ghafur (The Forgiving), Ar-Razzaq (The Provider), Al-Hakim (The All-Wise), Al-'Adl (The Just). Allah manifests the effects of His Names and Attributes in His creation however He wills. He creates, provides, shows mercy, forgives, guides, rewards and judges all according to His perfect wisdom and will. But we should be careful with the wording: Allah did not need creation in order to possess these Names and Attributes. He was eternally perfect before creation. Creation does not complete Allah; rather, creation displays the effects of His perfection. So when your mind asks, "But why did Allah choose to create us rather than not create us?", there comes a point where the answer is: Because Allah willed it, chose it, and in His perfect wisdom knew it was right to do so. We may understand some of the wisdom worship, mercy, testing, knowing Allah, rewarding the righteous, manifesting His Names and Attributes but we cannot demand a reason behind Allah's will as though something outside of Allah caused Him to choose it. Allah is the ultimate cause. There is nothing above Him compelling Him. So the question itself is not wrong. Thinking deeply about Allah is good. But eventually the believer reaches a beautiful limit: I know Allah is perfect. I know Allah is All-Wise. I know Allah needs nothing. I know He chose to create me. And even when I don't know every wisdom behind His choice, I trust the One who chose.