It is a fairly natural idea to have somebody fulfilling this role, and various Christian traditions have done just that. The following are from Worship music: a concise dictionary (ed. Edward Foley, 2000):
Cantor [Latin]. "Singer" (1) In Christianity, a 5th-century term for the psalmist; later, the medieval singer (often cleric) who intoned and led the chants; more recently a leader of congregational song who often sings the verses to the congregation's refrain. ...
Precentor [from Latin praecino, "I sing before"]. (1) The leader of chant in a schola; the precentor usually intoned chants on the side of the first choir, while the succentor ("subcantor") intoned for the second choir. (2) Another title for the cantor. (3) In some reformation traditions, the liturgical master of ceremonies, with special responsibility for the choral services. (4) The leader of congregational song in a church having neither a choir nor instrumental accompaniment.
Psalmist [Greek, Latin psalmista]. (1) One who leads (or sings the verses of) the psalm, usually in responsorial style. The term appears in the 4th century in some lists of ecclesiastical ministers. (2) The author of a Hebrew Bible psalm.
Psaltes (pl. psaltai) [Greek; Slavonic pevetz]. "Singer, cantor." In modern Byzantine usage when plainsong is used a psaltes or cantor ordinary leads the congregation by intoning and carrying the melody. In the Byzantine era (6th-15th centuries) Hagia Sophia had 2 choirs of psaltai; the leader (protopsaltes) stood between them. ...
In general, the lines seem to be a little blurred between the roles of "main singer" and "musical decision-maker", as with modern "worship leaders". The Orthodox protopsaltis seems to have evolved from the first into the second role. The Catholic Encyclopedia says under "precentor":
Anciently, the precentor had various duties: he was the first or leading chanter, who on Sundays and greater feasts intoned certain antiphons, psalms, hymns, responsories etc.; gave the pitch or tone to the bishop and dean at Mass (the succentor performing a similar office to the canons and clerks); recruited and taught the choir, directed its rehearsals and supervised its official functions; interpreted the rubrics and explained the ceremonies, ordered in a general way the Divine Office and sometimes composed desired hymns, sequences, and lessons of saints.
The Synod of Laodicea in the fourth century restricted who was allowed to sing:
Canon 15. No others shall sing in the Church, save only the canonical singers, who go up into the ambo and sing from a book.
This is probably connected to the idea of having a person in charge of planning and performing the music in general. I don't know who had that job before the dates given in the references above (which go from the fourth century to the medieval period).