The Sacraments of initiation (Baptism, Confirmation, and Eucharist), within the early Church, were never separated from one another. A believer was baptized, then confirmed, and then would receive Eucharist all in the same Liturgy, and this parallels priestly ordination within Leviticus (ritual washing, anointing, offering sacrifice). This is the reason why we start with Baptism. I think it best to remember this, wherein Eucharist is the culmination of Baptism.
All of the Sacraments find their meaning in Christ’s death and resurrection. I want explain every Sacrament, but…to be baptized meant to be “drowned” since this is how the word was used in pre-Christian writings. Within the Septuagint Old Testament, this word also meant “ritual washing.” Believers, therefore, were baptized, in their fallen nature, into Jesus at his death (submerged under the water) and are raised in him in his resurrection to be a new creation (coming out of the water). St. Paul, in this context, speaks of Baptism engrafting us into Christ’s Body. The Eucharist, however, is what makes the death of Jesus truly a sacrifice. It is what is called an anamnesis (a re-entry/re-presentation wherein we mystically enter into the same precious moment, literally) sacrifice, which, too, was at work while he was on the cross (the sour vinegar given to Jesus on the cross is actually cheap wine…this is the drinking of the Fourth Cup of the Passover ritual, the “cup of God’s Wrath”). I argue that the sacrifice, actually, isn’t fulfilled until the Emmaus resurrection Eucharist, but that’s another conversation. Confirmation is the Sacrament which shows, again, the healing of our former nature and the empowerment and authority of our new one…we are given spiritual Graces. Marriage also is similar to both Baptism and the Eucharist/Calvary (Christ gave himself for his Bride, the Church, “to wash her and make her pure” [Jewish marital custom of the Bride ritually washing before marriage], and she is his Body through his Eucharistic Body [just as Eve was the “body of Adam”…“bone of my bone, flesh of my flesh”]. In Confession, we “give glory” to Christ’s sacrifice for our sins, by confessing, in the case of mortal sin, our re-visited fallen nature, and we are raised, again, out of this, etc. Confession is not merely the reception of forgiveness, but the empowerment not to sin no more. But the Eucharist does this too.
You get the idea…all the Sacraments are extensions/dimensions of the Eucharist/Calvary, in different ways (I’m being very quick with my explanation, for the sake of time).
Baptism actually became valid long before even Jesus’ death. According to the Gospel of John, Jesus had the Apostles, already, baptizing people (again, anamnesis works in this case). This Baptism wasn’t the merely symbolic baptism of John. Jesus also washed the Apostles at the Last Supper, wherein he tells Peter, paraphrased, “if you don’t let me wash you, you have no Liturgical/Sacrificial Portion in me.”
The ultimate significance to the Eucharist, ultimately, is not only a re-humanization of our nature in Christ, since he shared our one shared human nature, but also our deification, since he shares with us his One Shared Divine Nature (shared with the Father and the Holy Spirit). “Christ became man so that men could become God.” While Baptism and Confirmation imprint a permanent seal on us that we belong exclusively to Christ, the Eucharist, however, does not only so that we can always continue to grow from Grace to Grace, from Faith to Faith. Yes, the Eucharist begins by atoning for all sin, and this is, normally established through Baptism and Confession, which depend on the Eucharist, which is their source, but the Eucharist ends in us “becoming partakers of the Divine Nature” (2 Peter 1:4).