How did God took flesh? St. Cyril of Alexandria

“We do not say that the nature of the Word was transformed into flesh, nor that it was transformed into a man composed of soul and body; we do assert that the Word, being hypostatically united to a body informed by a rational soul, in an ineffable and incomprehensible way, became man and was called “Son of Man”, not by his mere will and pleasure, nor by the assumption of a person; and we say that the natures are distinct, though they are joined in a true unity: yet then constitute a single Christ, a single Son; not in the sense that the diversity of the natures was taken away by the union, but in the sense that divinity and humanity, through their indescribable and hidden concourse, constitute a single Lord and Son, Jesus Christ.

Thus it can be affirmed that even though he subsisted before all ages and was generated by the Father, he was also generated by a woman according to the flesh. But that does not mean that his divine nature took its origin from the holy Virgin or that this nature needed a second birth after his birth from the Father (indeed, it would clearly be unreasonable and foolish to say that he who existed before all ages and who is coeternal with the Father had need of a second generation in order to exist). Rather, it means that, for our sake and for our salvation, he assumed his human nature into the unity of his Person and was born of a woman; this is why it is said that he was born according to the flesh. Therefore, we must not think that the holy Virgin gave birth to some unspecified man, into whom the Word descended later; no, we must believe that there was one single reality from the first moment in his Mother’s womb and that he was born according to the flesh, accepting the birth of his own body.”

Cyril of Alexandria, Letter II to Nestorius; PG 77, 44-49; ACO 1, 1, 1, 25-28