Who really 'painted' the original image of Our Lady of Guadalupe on Juan Diego's tilma?

The First Person of the Blessed Trinity, the Eternal Father, of course.
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"From the very beginning, and before time began, the eternal Father chose and prepared for his only-begotten Son a Mother in whom the Son of God would become incarnate and from whom, in the blessed fullness of time, he would be born into this world. Above all creatures did God so loved her that truly in her was the Father well pleased with singular delight. Therefore, far above all the angels and all the saints so wondrously did God endow her with the abundance of all heavenly gifts poured from the treasury of his divinity that this mother, ever absolutely free of all stain of sin, all fair and perfect, would possess that fullness of holy innocence and sanctity than which, under God, one cannot even imagine anything greater, and which, outside of God, no mind can succeed in comprehending fully.


Supreme Reason for the Privilege: The Divine Maternity

And indeed it was wholly fitting that so wonderful a mother should be ever resplendent with the glory of most sublime holiness and so completely free from all taint of original sin that she would triumph utterly over the ancient serpent. To her did the Father will to give his only-begotten Son -- the Son whom, equal to the Father and begotten by him, the Father loves from his heart -- and to give this Son in such a way that he would be the one and the same common Son of God the Father and of the Blessed Virgin Mary. It was she whom the Son himself chose to make his Mother and it was from her that the Holy Spirit willed and brought it about that he should be conceived and born from whom he himself proceeds.[1] - Ineffabilis Deus