The Father, the first person of the Trinity and the Fountainhead, reflects upon the sheer splendor of His own perfection. And being God, the Father does so perfectly. Thus, His reflection upon Himself, being flawless, is also wholly God. (I fancy at this point, the Father’s response upon perceiving Himself in the second person would’ve been to mutter under His breath: “Jesus Christ…”) Thus also, eternally existed the second person of the Trinity, the Only Begotten of the Father—the Son.
Both the Father and the Son love each other because they are both perfect. And both being God, they love each other perfectly. So naturally, they also (perfectly) love their Perfect Love. Thus too, eternally existed the third person of the Trinity, Love Himself*—the aptly named Holy Spirit.