I am interested in knowing when the term "Nativity" came into popular use for Christ's Advent and what are its origins.
In Catholic culture it comes from the Latin.
"Festum Nativitatis Domini Nostri Jesu Christi" (the Feast of the Nativity of Our Lord Jesus Christ) and the shorter form, "Dies Natalis Domini" (the Birthday of Our Lord).
From these Latin names most nations obtained their popular terms for the Christmas feast: "Il Natale" in Italy, "La Navidad" in Spain, "Natal" in Portugal, "Nadal" in southern France, "Nadolig" in Wales (and probably the Gaelic "Nollaig," as well). The Greek "Genethlia" means "Nativity," as do the names for Christmas in Hungarian ("Karacsony") and in most of the Slavic languages: "Boze Narodzenie" (God's Birth) in Polish; "Rozhdestvo Khrista" (Christ's Birth) in Russian and Ukrainian.
The French word Noel can be explained as either coming from the Latin "natalis" (birthday) or from the word "nowel" which means "news." In an old English Christmas verse the angel says:
I come from hevin to tell The best nowellis that ever befell.
It is possible that both explanations are right. "Noel" and "nowel" may be words of different origin that have become identical in meaning because they are pronounced the same. - History & Origin: Feast of the Nativity
The year 336 seems to be the first recorded date of Christmas at Rome.
The Nativity stories of Matthew and Luke are prominent in the gospels and early Christian writers suggested various dates for the anniversary. The first recorded Christmas celebration was in Rome in 336. - Wikipedia
Etymologically the word nativity came into use in the 12th century:
nativity (n.) c. 1200, from Old French nativité "birth" (12c.), from Late Latin nativitatem (nominative nativitas) "birth," from Latin nativus "born, native" (see native (adj.)). Late Old English had nativiteð, from earlier Old French nativited. - Dictionary.com, etymonline.com