My grandmother wrote an account of her journey as part of her citizenship training for the USA and I have attached it as a jpg at the end of this blog. In her account, she says she travelled to Koenigsburg (now called Kaliningrad) and then flew from there to Moscow to avoid travelling through (semi-independent) Latvia which wouldn't give her a visa. I checked this journey on the Eurorail site, they recommend a train to Prague where you take a train to Warsaw, from Warsaw you take a train to Vilnius in Latvia and from there you can get a train to Kaliningrad. It takes two days.
From Moscow she took the Trans-Siberian railway - a 9,000 kilometer journey. She wasn't allowed to take any money out of Germany so she paid for the whole thing in advance (they gave her vouchers to use on the train).