Did some Jews migrate to avoid the concentration camps?

Answer 1

Yes. However, by the time the 1930s had arrived, with the sudden spike in hatred of Jews by Germany, nationalism and border-control had also spiked, and people were suddenly unable to immigrate freely to the various destinations.America (for example), which had accepted 1,800,000 Jews before WW1, suddenly made a drastic reduction in the numbers permitted to arrive there. The same thing happened (for other reasons) in the British Mandate in Israel (Palestine).

The only place in the world to which Jews could enter uninhibited was Shanghai; and about 25,000 did so, despite the vast distance and the hardships involved. Even there, the Nazis badgered their Japanese allies to kill the new Jewish community.

Another point is that no one predicted that the Nazis would overrun all of Europe; so that Jews who did move out of Germany were killed anyway.

Also, the Nazis used a tactic of deception, right up to and including the last few minutes in the gas chambers which were presented as showers. Very few people were aware of what the Nazis were perpetrating. What was happening was unprecedented and inconceivable even as it was going on.