How can the existence of Allah (God) Almighty be proven, and the purpose of humanity's creation and life be explained, to a non-Muslim in a convincing manner?

Knowledge of God is consistent with innate human nature (fitra) and reason, and there are three types of proofs for His existence:

1. Innate Proofs: Every human being instinctively senses the existence of a Creator and turns to Him in times of hardship. 2. Empirical Proofs: The existence of cosmic phenomena: Creatures cannot come into existence by chance or create themselves; rather, they have a Creator who brought them into being, and that is Allah. Allah's perfection of things: Everything Allah created is perfectly suited for its purpose (e.g., camels for riding). The answering of supplications: Allah's answering of the Prophet's (peace be upon him) supplications is proof of His existence. 3. Legal/Scriptural Proofs: All divine laws indicate the existence of the Creator and the perfection of His knowledge, wisdom, and mercy, because they require a Lawgiver.

As for the reason for our creation, it is for the worship of Allah, giving Him thanks, remembering Him, and for our testing, as confirmed by His Almighty saying: ﴿He who created death and life to test you—which of you is best in deed—﴾ [Al-Mulk: 2], and His saying: ﴿And I did not create the jinn and mankind except to worship Me.﴾ [Adh-Dhāriyāt: 56].