A noun appearing as ᴱQ. nosta “birth, birthday” in the Qenya Lexicon of the 1910s derived from the early root ᴱ√NŌ “become, be born” (QL/66).
Neo-Quenya: As the root √NŌ survived in Tolkien’s later writings with very similar meanings, I’d retain ᴺQ. nosta for purposes of Neo-Quenya, but I’d limit its use to “birth”, and for “birthday” I’d use ᴺQ. nostarë.
Qenya cognate of Nos Duilin (PE15/22), a combination of nosse “people” and the genitive of tuilindo “swallow”.