From the beginning, literally, Gn 1:1, the Trinity is revealed to us. The Hebrew uses a plural word for God (Elohim) but pairs it with a singular verb. There were many attempted explanations over the centuries but only in Jesus do we see it fully explained. More specifically it is John ( 1 Jn 4:8) who explains it in three words
Θεός αγάπη έστιν - Theos agape estin- God is love.
If God is love there have to be two. After all, a person loving themselves completely is not love; it's narcissism. Love by definition requires an other. True love is also creative and so the love between the Father and the Son comes forth as the Holy Spirit. In the creed we say "who proceeds from the Father and the Son".
To call them "Creator, Redeeemer, and Santifcier" is just plain wrong because even in that first act of creation all three participated. Read Genesis Chapter 1 and the first chapter of John's Gospel.
If we listen to our prayers during mass, we will notice that they are almost always addressed to the Father, through the Son, and in the Holy Spirit. Only three times do we regularly address prayers to the Son: the Penitential Rite, the Peace prayers, and the prayers before communion (Lamb of God, Lord I am not worthy).
Years ago I worked with the deaf community, and there is some evidence to suggest that they have a more difficult time with abstraction. It was then that I conceived a way of thinking about the Trinity that at least works for me.
In prayer Jesus taught us to say, "Our Father who art in heaven" and so I locate the Father in heaven, a reminder that God exist outside time and space.
In every Cathoic Church there is the candle that burns 24/7 near the tabernacle to remind us that the Son is always there. Those prayers after the consecration and before we receive communion are addressed to the Son because by that point in the mass, he is present on the altar.
And of course St. Paul tells us that we are the temples of the Holy Spirit. So I can find the Holy Spirit in every baptized Christian in the world.
The truth is that no human words can explain the reality. It will always be, in this life, beyond our full comprehension. There are three and yet in everything they truly co-operate. They are one.
Even harder that comprehending the Triinity, may be living it. In John chapter 17 Jesus prays that we should be one as he and the father are one. And he made the unity possible by giving us the same spirit, the one Holy Spirit. As we celebrate the Trinity, may we strive to imitate the Trinity.