And that is an answer how?
Not sure how you didn’t get that.
Your term “mask” is perhaps causing you trouble. Three persons = three masks. It’s all semantics at a point.
God is One, the Infinite Being, et. al. “Immutable” as Soldier of God said (you kids are breaking off some of the rust from my metaphysical studies years ago). God revealed to us that God is Three Persons. So the point becomes, we only know that God is Three Persons
because God told us. We know that the Incarnation
is a fact, and we are left to puzzle out the mystery of how that is possible.
I try to think of the Incarnation in these terms. I prefer narrative because it works for me. You may not agree, but hear goes. It helps to think of it from God’s point of view, which is impossible, but let me elaborate.
*Imagine you are God/The Word/Paraclete, THE ONLY Infinite Being. Being Perfect and Love Overflowing, You Create as is your Divine Nature. You start with beings much like yourself, Spirit, and you figure that their minds can handle it, so you introduce to them, upon their creation, this plan you have. Not all of them think it is a good plan so you kick about a third of them out.
You haven’t created anything physical yet, and already there are problems with creating creatures of volition. Then you set the physical Universe in motion (big bang or not, the Universe is not infinite–only You are). Creation fits within a designated space, growing incrementally. Planets are formed, living creatures are created on (at least) one of those planets. You set up one race to be the steward race of all of them: humanity. The first humans disobey you, when you would have given them all of your graces, but they turned on you, too; one of the, let’s call them “angels” from Pre-Physical Creation; got to them and caused more trouble. Some punishmets are laid down, but the time will come when you will set things right again.
Then after a good deal of begetting, along comes Abram. Abram understands you as “Lord.” That’s fine for now. You reveal more and more of yourself and give hints to the generations that one day you’re going to come among them, and won’t that be just great!
Then the time comes when you, the Infinite, Immutable, Omnipresent consciousness, enter into your creation as one of them. You teach and found a church. Then before you defeat death on behalf of your creation, in this human body that you’ve poured yourself into, you tell your followers that your abiding presence will be called the Paraclete (changing names until in English it is one day rendered as “the Holy Spirit.”) *
Obviously this is imperfect, but as a paradigm it works for me. I tried to describe it this way when I taught CCD to 7th and 8th graders. The Word existed before Time, but the Word took
its acutal flesh and blood from Mary, which is how the Incarnation was possible.
There! Wasn’t that easy?