True. Waging aggressive wars were deemed to be a crime against humanity during the trials. There was no precedent for these trials, after all. However, waging an aggressive war has always been punished if the aggressor is on the losing side, as was the case here. The Nazi defendants could hardly plead that they didn't realize people would judge them for that.
Not entirely true. The Holocaust was exhaustively laid bare in the sense that the crimes were revealed in their full scope. There was little time to dig up all the bodies or to conduct a full forensic investigation, something which has still not been completed (we still find mass graves today). What was proved beyond reasonable doubt was that a genocide had been committed, and this was not denied by the accused - they opted to go for the "only following orders" defense.
(JW: Remember, they were not allowed to deny the general facts-only their personal involvement)
Lots of evidence was put forth, and it didn't confine itself to a single Soviet document. The Americans put forth thousands of confiscated documents, photos and films.
(JW:
Here's where the USHHM is playing fast and loose. The US collected 12 tons of documents overall. By the time the trial came about, the translators had only translated about 12,000. Of these 12,000...1,000 were cherry-picked and made available to the Defense and their whole case had to be presented from these.
The Soviets presented the Auschwitz case, not the Americans. There were no documents collected by the Americans that dealt with the Holocaust.
USSR-8 was created by a Soviet Commission, read into the court transcripts, and that was about it.
The Americans produced a film of (I think) Bergen Belsen, which was not a Death Camp. That was the film shown in the courtroom.
Given the amount of testimony and the fact that the testimonies were not the sole nor even the primary evidence, that the witnesses could not be cross examined made no difference. The mass of evidence was so huge that the accused never even attempted to deny that it happened.