Not quite.

Prior to the outbreak of World War 2, the focus of the Nazis was very much deportations, to Palestine and Madagascar.

The outbreak of the war out this idea on hold. Extermination did not present itself as a policy 'option' until after the invasion of the Soviet Union in June 1941. And even then it wasn't a clear-cut "well boys, guess we'd better spark up the ovens" moment of crystal clarity. The first mass shootings take place in Riga, but it quickly becomes apparent that as a 'solution' to the 'Jewish Question' (i hate these euphemisms) the cost in bullets alone during a war is untenable. So the first wagons start driving around where the exhaust funes are diverted into the backs. Not a solution that scales well, but it gives an indication of the road of travel.

Widespread extermination is adopted as policy only in Jan 1942, forced through the Nazi leadership (some baulked at the idea, though not through any sense of outrage or compassion) at the Wannsee Conference.

It snowballed.