I just did this last month with my partner and 2 kids. We didn't go as fast as possible, but took 5 days to let us break up the trip and see stuff along the way

I just did this last month with my partner and 2 kids. We didn't go as fast as possible, but took 5 days to let us break up the trip and see stuff along the way. We went from Amsterdam to Munich on day 1 via ICE trains (changing in Duisburg), had dinner at a biergarten and stayed overnight in Munich. Day 2 we explored Munich and that night got on the Nightjet sleeper train to Rome. Woke up in Italy on Day 3, enjoyed the views, arrived in Rome around 9 AM. Explored Rome , and stayed overnight. Took a Frecciargento train to Bari in Apulia on Day 4 and from there an overnight ferry to Patras in Greece, arriving Day 5. Took a taxi from there to Athens, which was pricey (€260) but sadly the trains don't run to Patras anymore and for our family this was a better option than the bus (and it was quicker, plus we stopped at Isthmia for souvlaki and to check out the canal.) Trains through the Balkans are not currently an option - they weren't running north of Thessaloniki even before COVID shut the borders. If you want to avoid flying or driving, you'll have to take a ferry from Italy to Greece. If we had to do it again, we might have taken the ferry from Venice or Ancona instead just because the port of Bari was so unwieldy for foot passengers and the Superfast I ferry was pretty bare bones and more geared towards truck drivers. Also, beware entry requirements to Greece, as they are constantly changing. Right now you couldn't actually do this trip because people arriving from the Netherlands have to show proof on arrival of a negative COVID test taken within the last 72 hours.