Making sense out of the Trinity. We don't just have to blindly accept it by faith, we can explaining it using reason.

1. In the the Trinity distinguishes between the principle of divine action and the subject of divine action. The principle of all divine action is the one undivided divine essence, but the subject of divine action is either Father, Son, or Holy Spirit. The Father can send the Son according to his power, and the Son can be incarnated according to his nature without dividing the divine essence.
2. 1. This comes mostly from Dr. Henry Morris. All physical reality has a dual nature. Mass and energy are in principle inter-convertible, through nuclear fission or fusion reactions. E = mc^2. We can, therefore, speak of the universe as a "space-light-time" universe. It is significant that this motion of light is famous for its mysterious and paradoxical complementarity. It has the characteristics of both waves and particles, and yet it definitely behaves as a wave motion under some conditions and as a particle motion under others. This duality applies both in radiations of electro-magnetic energy and in the atomic structure of matter, in which the orbiting electron likewise behaves both as a particle and as a wave. The two disciplines of modern physics known as quantum mechanics and wave mechanics have been developed from these two concepts.
3. Superposition. In quantum mechanics there is a principle called superposition, where subatomic particles are able to exist in two states at once.
4. Quantum Entanglement. For another potential scientific "validation" of such possibilities, in 2017 a group of quantum scientists (University of Science and Technology of China in Shanghai) successfully teleported a photon from earth to a satellite in orbit. It's called quantum entanglement. As far as our discussion here, quantum entanglement means that the two quantum objects share a wave function and share the same identity, even when separated. What happens to one happens to the other—whoever it exists. They are more than identical twins, the article said, "the two are one and the same." Apparently, according to the article, when they interact with matter on Earth they lose certain aspects of entanglement, but in the vacuum of space, they can extend infinitely (eternally).
5. From Sheldon Vanauken in his book "A Severe Mercy": Suppose I write a book about me. I am the main character in the book. The character in the book only says and does what I would say and do. That's me in the book. He’s exactly as I am, but at the same time the person in the book is a different person than the person who is the author. So in reality the "me" in the book and the "me" who is the writer of the book are separate persons, but we're the same essence. They're both me, but the two are distinct. I can easily be both the author and a character without compromising either.
6. From Dr. Joe Boot of the Ezra Institute: "If God is not the triune Lord revealed in Jesus Christ, then the doctrine of creation is rendered impossible, and man is part of a cosmic chain of being. This is because a monadic conception of God as some kind of singularity leaves us with the emptiness and void of non-personality as ultimate. If there is no plurality within God’s being, then there is no subject-object relationship, no particularity, only a blank unity. In such a view of God there can be no foundation for knowledge, love, morality, or ethics. Indeed, without an absolute personality, there is no diversity or distinction basic to reality at all; ultimate reality is a bare unity about which nothing may be said. This is why the Trinity is so important in tackling the philosophical problem of the one and the many. Moreover, because a denial of the Trinity leads to a denial of an absolute personality, we cannot speak coherently of the will of God. Only persons have a will. But if God has no will, then creation is not the free act of an absolute, personal God. Rather, the universe is the emanation of divine being, and what we call the universe is merely the extension of god, or, as some pagans would say, it is the body of god."

The Trinity is hinted at in the Old Testament.

Jesus teaches the Trinity.

Paul teaches the Trinity.