Question

When did the final stage of the Final Solution begin?

Answer 1

It depends on what you define as the final stage because it was an ongoing process.

Explanation:

I would argue that the Wannsee Conference held in a suburb of Berlin on January 20th 1942 could be seen as the beginning of the final stage. Already there had been mass murders of Jews in the East after Operation Barbarossa in June 1941. These were carried out both by Einsatzgruppen killing squads, elements of the Wehrmacht and local militias.
At Wannsee a meeting was held of senior officials to coordinate the Final Solution. The meeting was chaired by Reinhard Heydrich and the minutes taken by Adolf Eichmann.