Do Bible trinitarians believe God's self revelation to humanity began with the Father and is currently being completed by the Spirit?

Since the Father is the most supreme hierarchical being in the trinity, followed by the Son and the Spirit, does it mean that the self-revelation of God to man was started by the Father in the Old Testament , succeeded by the Son who died on the cross to take away the sins of the world, then succeeded by the Spirit who is completing the works of salvation, and if the spirit is completing the works as the most junior member of the trinity then it means it was began by the most senior member of the trinity, what do Bible Trinitarians think? Did all the three equally participate in salvation as they all participated in the creation of the world?