When exactly were the initial death toll figures calculated? Within a few months of the wars end isn't precise enough. The earliest report of six million Jews dead I have seen was in January 1945. Six million Jews were predicted to be dead in 1943. Six million Jews in peril predates the war.
With the massive upheaval caused by the major combat operations, the huge numbers of civilians fleeing the Red Army, and the Russian's refusal to allow the Western allies into the territory overrun by the Red Army it would have been impossible to gather any meaningful data during the final months of the war.
You're presuming, wrongly, that the total is actually six million and that demographic research hasn't advanced since 1945, both of which are false.
In actual fact the situation of the Jewish population of Europe had been tracked by news reports throughout the entire war. Organisations like the Institute for Jewish Affairs as well as the editors of American Jewish Yearbook took note of all the border changes and occupations, and once the major population displacements started, they received a great deal of information, both from the Axis press as well as underground reports. The Slovaks were entirely open about how many Jews they had deported in 1942, and publicised the figure in their press, for example.
Once extensive reports of killings began to come through, then you can easily find global estimates, starting with 1 million in mid-1942, then 2 million dead being estimated at the end of 1942, then in August 1943, the Institute of Jewish Affairs estimated 3 million dead, and broke down the totals by countries, giving figures for numbers displaced/deported/fled and numbers killed.
By the spring of 1944, there were reports in neutral and Allied countries picking up on a story run in a Nazi newspaper claiming 5 million had been got rid of - given all the other evidence that was accumulating this was understood to mean 'killed'.
In the summer of 1944, virtually all of the occupied Soviet Union was liberated, and Poland was overrun up to the Vistula, i.e. the Lublin district was liberated, and the camps there were exposed. This coincided with reports out of Auschwitz talking of very large numbers killed there - the Vrba-Wetzler report spoke (wrongly) of 1.715 million, before you even count the Hungarian Jews.
By this time, it was apparent to interested observers that the Jewish population on Nazi-occupied Soviet territories had been entirely wiped out other than small handfuls in hiding. The Soviet authorities registered those survivors as part of their reimposition of Soviet control on especially, the territories annexed in 1939-40. So you have some stats being reported in the western press on how few survivors there were in whole districts. But there was also still a great deal of uncertainty as to how many had survived by fleeing ahead of the occupation.
If you read the press in the first five months of 1945 you'll find quite a few reports discussing the number of survivors left in this or that country, or town. Only a tiny number were left in Lodz, for example (some who had been in hiding and the clean-up crew in the ghetto - less than 1,000).
The Institute for Jewish Affairs wrote
a 16 page report synthesising all these different reports in June 1945. All the sources for their estimates are specified, and they emphasise the uncertainties. They also emphasise and estimate the numbers of survivors who were in Germany and who had been evacuated to the east in the Soviet Union.
Those figures are estimates. No one has pretended otherwise. The figures are also straight demographic balance sheets. You can easily see where the estimates went wrong (eg Belgium) and where they were close to the eventual mark. The figures for Poland are a slight underestimate, something caused by inflated estimates of the number evacuated to the interior of the USSR. We now have the precise figures, so we can prove this was inflated somewhat. The figure for Hungary (Trianon Hungary) is a slight understatement as well. The Netherlands are underestimated by 35,000 compared to the subsequent Dutch Red Cross investigation. The Soviet total is close to the accurate number for the
demographic loss, once you include Jewish soldiers killed in action
Overall, the estimates are actually pretty good, all things considered. You can subtract there and add here, but there was sufficient data to project an overall demographic loss of 5.7 million, which is close to the most probable total for the total loss. Since the actual loss to mass murder and crimes against humanity was 5.1-5.3 million, there is already a fair bit of room to account for other demographic losses like war casualties.
Obviously, as things settled down, better data became available, and it was also possible to establish how many had been deported, who had returned, etc. It didn't take long for the Belgian government to work out that 24,000 Jews had been deported from their country, whereas only a thousand or so had returned. Ditto with the French. They initially overestimated the number deported, then corrected this, then worked out how many had returned.
Most countries in western Europe had temporary ministries for refugee affairs, because Jews were far from the only people who had been displaced by the war. Most countries had seen political prisoners deported en masse, and virtually all had seen massive numbers of civilian workers deported, along with contingents of POWs who were retained by the Nazis for labour in the Reich.
The Soviets and Poles also had their own commissions for repatriation and were quite keen to register their populations properly. The Jewish community in Poland kept very extensive records from the spring of 1945 onwards, and these track the return of Polish Jews from the USSR, as well as the exodus westward which accelerated in 1946. The same group of people were really being counted four times. They were evacuated or deported by the Soviets in 1940-41, then returned to Poland in 1945-46, then left for the west from 1946.
That's something which has been obvious since 1945 to all interested and informed observers, but of course it's understandable if troglodytes want to treble-count the same people in order to sustain their politically motivated feeble attempts to revise history. That said, I don't see any kind of balance-sheet being offered by any of the deniers on this thread, who seem to be denier-numerate only, whereby every number is always six million subtracted by six million.
The eventual 'triumph' of Six Million was of course the result of the IMT judgement citing Hoettl's guesstimate, and it is naturally a Very Bad Thing that popular consciousness repeats this figure when in fact it is more like 5.1 to 5.3 million. But then popular consciousness seems to believe that "Stalin killed 20 million" or that "communism killed 100 million" without ever bothering to check on the real numbers.