For the TNG episode of the same name, please see "Firstborn".
A firstborn was one's first child.
Audrid Dax rated becoming head of the Symbiosis Commission as being the second best day of her life, second to giving birth to her first child. (DS9: "Facets")
The Albino promised to take his revenge on the firstborn of Kor, Koloth, and Kang in 2290 and did so a few years afterward. (DS9: "Blood Oath")
In 2366, Data questioned whether Vice admiral Anthony Haftel, (who felt the android did not have the ability to parent Lal) had experience as a parent when his first child was born. (TNG: "The Offspring")
In 2369, "Rumpelstiltskin" asked Miles O'Brien if Molly was indeed his firstborn. (DS9: "If Wishes Were Horses")
In 2375, Quark wondered whether Jadzia Dax had wanted to name her first child after him. (DS9: "Shadows and Symbols")
In 2378, Kathryn Janeway told Q that she was flattered that he would entrust his firstborn to her, but that she didn't have time to educate him on humanity. (VOY: "Q2")