I had newly found and was exploring this concept of European night trains only last week so don't have concrete experience with planning this yet, but I did see

I had newly found and was exploring this concept of European night trains only last week so don't have concrete experience with planning this yet, but I did see notes in some places that you can disembark until 7am even if the train arrived at 5:something am already. If it drives only from 23:00--02:00 then I'd imagine you're out of luck indeed, but they do accommodate this problem in some cases.