Wilhelm Höttl, SS man and famous opportunist, used the 6 million number very early, in 1945, claiming the number was talked about with Eichmann.

Modern understanding of the Shoah includes figures from NS documents combined with approximations and surveys of pre-war census numbers. While the persecution if Jewish people in the Reich and in the west (like in Holland and France) was meticulously documented, the big numbers resulting from the annihilation of the Eastern European Jewish communities are far harder to ascertain.

EDIT: i'm now thinking about your use of the word "realized". As I said above, the public knew that we're talking about millions and millions almost immediatly after the end of the war. But it took the societies more like decades to actively try to come to terms with these numbers. TV series like Holocaust from 1978 and Claude Lanzmann's Shoah from 1985 were important landmarks for this realization, among many other breaks and changes in the public discourse.