Albert Einstein, being a renowned physicist, was indeed well-known internationally, including in Nazi Germany. However, the circumstances surrounding Einstein's departure from Nazi Germany were not a simple matter of escape.
In 1933, when Adolf Hitler and the Nazis came to power, Einstein was visiting the United States. Given his Jewish heritage and outspoken criticism of the Nazi regime, he decided not to return to Germany. The Nazis considered Einstein's work as "Jewish physics" and sought to suppress his ideas. They also confiscated his property and revoked his German citizenship.
While the Nazis were aware of Einstein's departure and his opposition to their ideology, it wasn't a matter of allowing him to escape. Einstein left Germany voluntarily due to the increasingly hostile environment for Jews and intellectuals under the Nazi regime. He sought refuge in the United States and became a professor at Princeton University, where he continued his scientific research and activism.
It's worth noting that the circumstances surrounding Einstein's departure were complex, and many factors influenced his decision to leave Germany. However, it wasn't a case of the Nazis deliberately permitting him to escape due to ignorance of his identity or significance.