Nope. Austria was March 1938.
You are looking for Poland, September 1, 1939.
The Austrians LOVED Hitler and the German Army. Accounting for population, there were more SS-men from Austria than Germany. Eichmann was from Austria. Skorzeny and Kaltenbrunner were Austrians. Hitler, of course, was born and raised in Austria.
It was joyous Austrians who tore down the border barriers, strew rose petals on the ground to welcome the Wehrmacht, who welcomed Hitler to Vienna with loud hosannas.
There is a very common saying: "The Austrians are very clever, to convince the world that Beethoven was an Austrian and Hitler was a German".
I think that had Hitler been forced to stay within his own borders, the war would have either started earlier, or not at all.