There is some kind of fundamental communion already, albeit imperfect, and as the Church prepares to welcome you as a candidate for reception into full communion with us, St. Curious, we share your joy, and look forward to the day when you will share fully with us at the altar of the Lord’s Eucharist.
Baptism as a Lutheran does incorporate someone into Christ and makes that person a member of the people of God, but not in a way that establishes full communion with the Catholic Church. (Canon 204 “§1. The Christian faithful are those who, inasmuch as they have been incorporated in Christ through baptism, have been constituted as the people of God.”)
Full communion requires something additional according to canon 205, “Those baptized are fully in communion with the Catholic Church on this earth who are joined with Christ in its visible structure by the bonds of profession of faith, the sacraments and ecclesiastical governance.”
So as others have noted, a profession of faith is required to enter into full communion with the Catholic Church.
Confirmation does not effect full communion with the Church, but it is part of full initiation. It’s a small but important though confusing distinction (Canon 842: “§1. A person who has not received baptism cannot be validly admitted to the other sacraments. §2. The sacraments of baptism, confirmation, and the Most Holy Eucharist are interrelated in such a way that they are required for full Christian initiation.”)
Only in that sense, could we say that" no one is a full member of the Catholic Church until being confirmed" and Eucharistized. Hence, for example, a child who is baptized Catholic but not yet confirmed is still in full communion with the Church, although the child is not yet fully initiated into it until those sacraments of Eucharist and Confirmation are received.