All believers have a "first Communion" in the sense that there was a first time they took the Lord's Supper, but what significance does or should this event have? The Bible does not ever discuss the first time a person takes Communion. However, it does discuss the great importance and significance of Communion itself, implying that it is indeed a special event. It is certainly not wrong to celebrate a person's first time participating in this important part of the Christian life, and even appropriate due to its special nature.
Is the celebration of a first Communion / Eucharist biblical?
In Eastern Orthodox and Roman Catholic practice, a first Communion is observed during a ceremony as a special occasion in either a new adult believer's or child's life. In the Roman Catholic and Eastern Orthodox churches, these observances or celebrations are based on a misunderstanding of the Lord's Supper and how salvation is accomplished, and therefore served to children who may or may not have believed on Jesus Christ as their savior, a biblically prescribed prerequisite for participation in Communion. Ceremonies such as these are not biblical simply because of their incorrect view of Communion and salvation, not because celebrating the first time a person takes Communion is wrong in itself.
Anglican and Lutheran churches (two Protestant denominations) have ceremonies similar in format to those practiced by the Roman Catholic Church. Again, it is not the ceremony that is unbiblical, but the understanding of Communion. If the church, or that particular church's priest, has a solid understanding of Communion and has vetted the new believers and children properly, then there is nothing wrong with such a ceremony, though neither is it necessary.
What is the significance of the Lord's Supper?
What is the biblical frequency of Communion?
Is Communion supposed to be open or closed?
Is Sabbath-keeping something Christians should do?
Is there a correct mode of baptism?
Truth about Church