Three Is the Loveliest Number
This is precisely why the apostle John can write that "God is love" (1 John 4:8, emphasis added), for this God would not be who he is if he did not love. If at any time the Father did not have a Son to whom he gave his life and love, then he simply would not be a Father. To be who he is, then, this God must give out life and love. And so we begin to see why the Trinity is such good news: God is love because God is a Trinity, because for eternity this God has been giving out—positively bursting with—love for his Son.
How the Father loves and delights in his Son is something we get to see in the baptism of Jesus. There the Father declares his love for his Son and his pleasure in him as the Spirit rests on the Son like a dove. For the Spirit is the one who makes the love of the Father known, causing the Son to cry "Abba!" (see also Romans 8:15 and Galatians 4:6 for how he does the same for the adopted children of God). Thus Jesus is called "the Anointed One" ("the Messiah" in Hebrew, "the Christ" in Greek), for the Father loves, blesses, and empowers him by anointing him with his Spirit.
All of which is to say, briefly, that when you start with the Jesus of the Bible, you inevitably arrive at a triune God. John wrote his gospel, he tells us, "that you may believe that Jesus is the Messiah, the Son of God, and that by believing you may have life in his name" (John 20:31). But even that simplest call to faith in Jesus is an invitation to a Trinitarian faith: Jesus is described as the Son of God. God is his Father. And he is the Messiah, the one anointed with the Spirit.
Yet while Jesus does reveal a triune God, this triune God that he makes known does not come across as anything like a philosophical headache. Here is a God who is delightfully different from all others, a God who is love: a Father, loving and giving life to his Son in the fellowship of the Spirit.
A Far Sweeter Gospel
To taste the difference the triune nature of God makes, let's step back for a moment and imagine something. What if God was not Father, Son, and Spirit? What if God was really just a single person? Well then, for eternity before Creation he must have been all by himself: no relationship, and nobody and nothing else for him to love. For eternity. This God simply could not have love at the very core of his identity. So would he be the sort of God inclined to be gracious toward us? Most unlikely. And, not having ever known fellowship himself, would he want to have fellowship with us? Would he even know what fellowship means? By definition, a single-person God is not inherently about love and relationship; its "gospel" must be a very poor thing next to the gospel of the God who is love.
But with the triune God, what good news we have! The eternally beloved Son, the delight and joy of his Father, comes to share with us the same love the Father has always given him. He comes from "the bosom of the Father" (John 1:18, NASB), announcing his desire that believers might be with him there (John 17:24), that we might be brought before the Most High—not just as forgiven sinners, but as dearly beloved children sharing the Son's own "Abba!" cry. Because God is Father, Son, and Spirit—and only because God is Father, Son, and Spirit—we can bask in those gorgeous words of the Son to his Father: "you … have loved them even as you have loved me" (John 17:23). The Father's eternal love for the Son now encompasses us. Thus with this God we have a gospel better even than forgiveness—we can have the security and intimacy of children. Beloved children of the Most High! No other God could bring us so close and have us so loved; no other God could so win our hearts.