Green’s Dictionary of Slang

(US) to show off, to try to impress; thus big talker n., one who boasts; big-talking adj., boastful.

1902		O. Wister Virginian 85: They are always big talkers on Bear Creek.
1940		Davis & Dollard Children of Bondage 211: Judy admits that he is a ‘big talker’ and that he runs from good fighters.
1951		R. Bissell Stretch on River 14: Don’t try and big talk the other deckhands [W&F].
1956		E. Pound (trans.) Sophocles’ Women of Trachis 14: That’s what comes of big talk [...] Hell’s full of big talkers.
1958		A. Sillitoe Sat. Night and Sun. Morning 7: He begrudged big talkers their unearned glory.
1960		G. Swarthout Where the Boys Are 34: This Thompson big-talker.
1999		J. Ridley Love Is a Racket 231: I big-talked and tough-guyed my way through the day.
2004		(con. 1988) N. ‘Razor’ Smith A Few Kind Words and a Loaded Gun 321: It wasn’t the first time I had been left out on a limb by big-talking wankers.
2015		S. King Finders Keepers (2016) 59: I’m not a cowardly big-talking homo either.