The word "person" doesn't actually occur in the creed, but the word the fathers used in Greek is either /prosopon/ or /hypostasis/. The word prosopon can mean mask, or just face, or the visible outward manifestation of a being.
This is contrasted with "ousia," which is the underlying deeper reality or nature.
The doctrine of the Trinity is simply that God is one ousia and three hypostases/prosopa. Father, Son, and Holy Spirit are each totally God from all eternity, but they are still distinct in their personhood. The Athanasian creed said that the Father is God, the Son is God, and the Holy Spirit is God, but there are not three gods but one God. The Father is not the Son, the Son is not the Spirit, and the Spirit is not the Father.
God is therefore One, and is at the same time an eternal community of perfect love.
Thank you for the clarification.