Shortest ever? Mid-game.
* On **Oct 16, 1921**, Rock Island Independents player-coach **Frank Coughlin** was **fired during the game** and immediately replaced by Jimmy Conzelman — the only known mid-game head-coach firing in NFL/APFA history. ([Pro Football Researchers][1])
If you meant modern timing benchmarks:
* **Before the regular season:** the Rams fired **George Allen** **after just two preseason games** in **August 1978**. ([The Washington Post][2])
* **Earliest in a regular season:** coaches have been dumped **after two games**, e.g., **Joe Collier (Bills, 196

** and **Jack Patera (Seahawks, 1982)**. ([Wikipedia][3])
So the literal earliest is *mid-game* (1921); in the modern era it’s as soon as **Week 2**.