In a parallel equivalence, the intrinsic Divine Substance cannot be separated from any of its three Manifestations: Father, Son and Holy Ghost.
Thus, since the Second Person of the Most Holy Trinity, Jesus Christ, cannot be separated from its Divine Substance, it follows that:
The Divine Motherhood of Mary is a concrete reality not requiring a separate act of Faith.
Of course, Mary is not the First Cause. The Father, the unCreated Creator, is the First Cause. Nonetheless, by being the Mother of the Son of God, Jesus, Who Is the Word of God in the flesh, justifies calling Her Mother of God as long as we do not subconsciously place Her above God.
To deny this parallel would imply that a mother is only the mother of the body of a child and not of the integrated human being born from her. That is a complete impossibility.
It also logically follows that God-manifested-in-the-flesh, Jesus Christ, could not be formed within an impure woman, thus Mary's Purity had to be of body and soul; thus, She was Immaculately conceived, i.e., Her soul was not stained by the original sin.
Naturally, Her Heart had to truly be Immaculate. We did not need a Dogma nineteen hundred years later to establish that. Even in the Muslim Qur'an - since the seventh century - Mary is identified as an Immaculate woman [Sura iii. 42].
It really is That Simple!
(1) Most Holy Trinity