I'm assuming that in many places that education was suspended, that education was probably not the highest priority at the time. How long did it take to reestablish education (primary, secondary, and university) in those areas?
Well, in Poland situation was a bit of an outlier, as in general Poles were discouraged to have any kind of education. Himmler famously said that a Pole should only be able to sign his own name and count to 500. The only schools that remained open in Poland were trade schools.
Many of Poland's intellectuals were persecuted starting from day 1 - immediately after taking Krakow, Nazis sent the professors of Jagiellonian University to Auschwitz and other concentration camps. (not to confuse, Auschwitz then was not a death camp yet, even though a lot of professors had Jewish background).
Teachers and other intellectuals were not allowed to work, whether in their chosen field or otherwise. If they managed to obtain false documents, they typically took up menial work and many of them taught in secrecy, even despite death penalty for teaching. After the war around a million such students and graduates were accepted by the Polish universities.
However, end of the war did not mean end of repression. Stalinist Soviet Union had strict ideological requirements, and all the subjects had to conform to the marxist interpretation. This caused firing many professors and students, and promotion of students for "social background", for instance sons of farmers and workers received extra credit.
And of course, after the war the country needed new teachers and engineers - besides pre-war professors new teachers were educated in high-schools, which had a reputation of producing pseudo-intellectuals. It was only in 1960s that Poland's education began to recover from WWII, but of course the communist ideology, combined with anti-semitic cleanses of 1968, continued to hinder the education policies.