It depended heavily on where someone was. For some it was a period of years, for others it was less than a week. Those who had the most time were German Jews. From 1933-1935 their lives had some normality, though persecution was increasing. In 1935 the Nuremberg Laws were passed, which heavily curtailed Jewish rights, and took away Jewish citizenship. Street violence became slowly more and more normal, and in 1938 the Kristallnacht pogrom became an indication of mass violence to come. Some German Jews were deported to ghettos in Poland during 1940-41 (approximately). Deportations to sites of mass killings became common only in 1942-43. This meant that there was approximately a decade of living under Nazi rule before the German Jewish population was murdered. It is no coincidence that German Jews were the most likely to have been able to emigrate from Europe prior to the Holocaust. They were also most likely to be internally displaced within Europe and still faced murder. The most famous example would be Anne Frank, who was German, but with the Nazi rise to power her family left for Amsterdam. There they stayed in relative security until the war began. Then the persecution began to increase, and once the family feared for their lives they went into hiding, which was in 1942, when deportations from the Netherlands to death camps in Poland began.

In the areas of Poland which came under Nazi control in 1939 there were between two and four years before the majority of the population had been killed. About 90% of Polish Jews were murdered and they made up about half of the victims of the Holocaust (about three million of the approx. 6 million victims). In the areas of the General Government (Western Poland) there was often a process of ghettoization, where the Jewish population was segregated. Ghettos were already a place of mass death by about 1940-41, but it was due to disease, starvation, and seemingly random executions. Deportation to killing centers began in 1942, and were primarily to death camps where people were killed within hours of arrival.

In other areas under Nazi control there was almost no time between when an area came under Nazi control and when murder of Jews began. In the areas taken during Operation Barbarossa murder actions would sometimes precede things like ghettoization, such as in areas of Lithuania where murder was carried out by Germans and locals immediately in the summer of 1941. This means that prior to the creation of places like the Vilna (Vilnius) and Kovno (Kaunas) ghettos, and before the murder actions in the ghettos and deportations to killing centers (either by mass shooting or gas), Jews already were well aware that the Nazis intended to kill them.

In many areas of the former Soviet Union, as well as places like Ukraine and Belarus mass murder was carried out soon after the German invasion. For example the Germans took control of Kiev in September of 1941, taking full control of the city on September 26. Just three days later the Babi Yar massacre began just outside the city, in a matter of days tens of thousands of Jews had been murdered.

In Hungary too, the murder happened very quickly. In less than two months in summer of 1944 the majority of the population was murdered in Auschwitz. Hungary had only come under direct Nazi occupation a matter of months before.

The Holocaust was carried out in extremely diverse ways, simply because it was carried out in such different locations, against varied populations. In some areas it happened extremely quickly, in other places it was a slow process.

Just to add to u/PeculiarLeah’s very detailed post, I would like to add that while in some cases the majority of Jews in some environments were not murdered quite so quickly as in others, such as Jews from Western Europe and Germany compared to the Soviet Jews, that is not to say that deaths were uncommon.

Even before the enactment of the specifically genocidal ‘final solution’, Jews were often subjected to shootings, starvation, forced resettlement, and reprisals generally disproportionately to other groups. Generally within Nazi policy, even before it had been decided to kill all the Jews, their death was still seen as advantageous.

For example in September 1939 the T4 euthanasia programme was begun, which forcibly euthanised many physically and mentally disabled individuals. Within the bureaucratic framework through which it was decided who was to be killed during this programme, being Jewish wouldn’t often tip the scales. For example, in the case that two individuals were patients at a medical facility, with the same illness and chances of recovery, the only difference being that one was Jewish and the other not, the Jewish individual would be much more likely to be killed.

So while generally speaking some Jews may have had ‘more time’, and this may be true for the whole, it is not always true for individuals who may tragically have not. So for some, the danger of a situation could change incredibly rapidly, while for others it may not change so quick, even within the same area.