So many people died in the conflict and it is known that Treblinka was almost wiped off the map and in the records by the Nazis and almost went unnoticed. This camp exterminated about 1.6 million people and only had a handful of survivors. However, these handful of survivors wouldn't have known the total number. This is the same for other camps such as Auschwitz.
So how long did it take for people to count up the numbers?
Or a better way of phrasing this: how long did it take them to know the true number?
Well to start off we have a noticeable err here. Treblinka didn't 'exterminate' 1.6 million people but was part of a Nazi program of extermination and looting titled 'Einsatz Reinhardt' - later to earn the name 'Aktion Reinhard/t'. Based on modern research 'Einsatz Reinhardt' exterminated around 1.4 million Jews. (Belzec: 440,823-453,021 Sobibor: 170,165 Treblinka: 780,863) Anyway it should be noted that its impossible to answer your second question because there is no "true number". The 'six million figure' has multiple origins from testimony at Nuremberg to a rounding up of Anglo-American Committee of Inquiry's findings from 1946 which generated a death toll of 5.7 million. In the same year Jacob Lastchinsky reached a higher figure of 5.9 million. Both can be found in the appendices of Nora Levin's "The Holocaust". So it seems figures were generated immediately in the wars aftermath.
Sources: Peter Writte, Stephen Tyas, A New Document on the Deportation and Murder of Jews during “Einsatz Reinhardt” 1942, Holocaust and Genocide Studies, Volume 15, Issue 3, Winter 2001, Pages 468–486
Musial, B. (2004). "Aktion Reinhardt": Der Völkermord an den Juden im Generalgouvernement 1941-1944.
Schelvis, J., Moore, B., Dixon, K., & United States Holocaust Memorial Museum. (2007). Sobibor: A history of a Nazi death camp.
Kuwałek, R., Hänschen, S., & Loose, I. (2013). Das Vernichtungslager Bełżec.
Levin, N., & Mazal Holocaust Collection. (1968). The holocaust: The destruction of European Jewry, 1933-1945.