This photo (from the German Bundesarchiv) captures an SS execution of Poles in Kornik just weeks into the German occupation of Poland in 1939, fruit of a pre-planned Nazi project to secure the new territory as lebensraum.
Operation Tannenberg (English Wikipedia entry | German | Polish) could be seen as a vanguard for the mind-boggling exterminations to come in subsequent years, cementing the army’s commitment to a campaign that extended well beyond territorial conquest. Alexander Rossino examines this understudied segment of World War II in Hitler Strikes Poland: Blitzkrieg, Ideology, and Atrocity and contends that “the unlimited, almost nihilistic violence of the Wehrmacht” emerges first in these initial weeks of the Polish campaign, which proved a “transitional conflict” pivoting towards the more notorious atrocities to come. “The invasion of Poland thus occupies a crucial place in the history of Nazi Germany’s descent into mass murder and genocide.”
Drawn up by Hitler, Himmler, and Heydrich and officially authorized on August 25, a week before Germany invaded Poland, Tannenberg intended to destroy Poland’s elites — from intelligentsia and nobility down to community priests and teachers, and the politically active across the spectrum from Communist to monarchist. The hope was to leave the subject nation supine, incapable of challenging Berlin’s designs on her future. Estimates I have seen vary widely but tens of thousands of Poles (with a liberal portion of Polish Jews) were shot by SS Einsatzgruppen units under Tannenberg even by the end of 1939, and kilings continued apace thereafter. Though not the literal first Operation Tannenberg Killings, the October 20-23 period marked the first public mass executions; a Polish-language list of the incidents and victims involved is available here.
The very name Tannenberg is a nationalist allusion to Germany’s time-immemorial rivalry with Poland; the original Battle of Tannenberg saw the rising Polish-Lithuanian empire defeat the Teutonic Knights, essentially breaking the latter as a European power. This defeat resonated in 20th century German national mythology not unlike the Battle of Kosovo for Serbia; in 1914, Field Marshal Paul von Hindenburg made himself a household name by smashing the Russians in a battle vaguely in the vicinity, and cannily christened it, too, the Battle of Tannenberg. (The Germans put up a monument to it which they felt obliged to tear down later in the war as they were being driven out of Poland.)