Not only is the Scriptural basis of the Trinity solid (see here and here, for example), but the concept makes sense. For example, it enables the eternity of love, making it easy to understand how love could exist even before the Creation: The three elements of the Trinity could love one another.
And the Trinity also makes sense because it is a reflection of God’s three main roles. He is the Father, the ultimate authority figure, the Executive of Creation. The Holy Spirit is everywhere, always, and always advancing God’s will.
And the Son? Well, His focus is on people, human beings — us. We are special to God. The Son is also eternal and had a pre-human role (see John 1:1-5). But throughout the Bible — in the New Testament, of course, but even in His Old Testament appearances — His specialty is HR. He taught us, saved us, is our advocate, and will judge us.