It started with people conveniently far away: Africans and Native Americans. Genocide against them was incredibly profitable. This made the empires of Spain, Portugal, UK, Belgium, and France. The Axis countries were trying to acquire a similar empire at a later date, and therefore had to create a racial enemy out of those they wanted to conquer; Italy in Abyssinia, and Germany against the slavic peoples to the east. The Jewish people (and Romani, disabled, queer and other groups targeted) were a convenient internal enemy. Fascism relies on enemies to unify the "people" against.
Allegedly Hitler said "nobody remembers the Armenians" when asked about genocide, referring to the comparatively recent event: https://en.wikipedia.org/wiki/Armenian_Genocide
The Holocaust of the Jews was the point at which the horror was brought home enough that most people could recognise it as morally abhorrent, and there was enough "never again" motivation to embed human rights into the https://en.wikipedia.org/wiki/European_Convention_on_Human_R... .