Jewish communities in Europe trace their roots to Israel/Judea and the Roman expulsion and subsequent colonization.

Israel nowadays is mostly non-Ashkenazi in any case, and is mostly composed of Jews ethnically cleansed from Arab countries following the 1948 war

There's a widespread antisemitic conspiracy theory which links Ashkenazi to Khazars, but except being historically unsound, it echoes very ancient antisemitic (racist) tropes such as British Israelism, which are christian ideas claiming Jews are imposters to their own religion/nationality

No, actually every single Israeli prime minister is in fact Eastern European. They even changed their names to sound more "hebrew", which itself is an affected language created for propaganda purposes.