I cannot write a realistic non-hand-wavy design document without having a proof of concept working, because even if I try, I will need to convince myself that this part and this part and that part will work, and the only way to do it is to write an actual code, and then you pretty much have code ready, so why bother writing a design doc.

Some of my best (in terms of perf consequences) design documents were either completely trivial from the code complexity point of view, so that I did not actually need to write the code to see the system working, or were written after I already had a quick and dirty implementation working.