This is not easy to tell, but I'll give it a try.
The German Wikipedia article about the DAX contains a reference to a historical extrapolation of the CDAX:
(On https://de.wikipedia.org/wiki/Wirtschaft_Deutschlands, more index values can be found from this era.)
Assume your hypothetical index fund wouldn't have any fees nor tracking error, so the fund develops exactly as the index itself.
We see the price take a big hit down to about 1.5 soon after. Then it recovers a bit to over 8, take another hit down below 4 during the Great Depression and then recovering again until the end of WW II to about 12.
Then another big hit comes and takes us down to about 3. Only the "Wirtschaftswunder" (economic miracle) takes us up again, crossing the line of 6 (where we started from) even before 1950. From then on, this line is never crossed again.
Considering only these 30 years, we are more or less as wealthy as before, but we have survived the Great Inflation of 1923, the Great Depression and WW II. During these 30 years, where were two monetary reforms have taken place, taking away most savings from the German citizens. So we have managed to at least keep our wealth.
If we are able to keep our investmens for a while, after the "Golden 1950s" our investments are about ten times higher, about 64.
In comparison to keeping cash, we managed to keep the investment instead of losing it in the Great Inflation, where in the end 1 trillion ℳ was exchanged to 1 ℛℳ. 1948, the second monetary reform roughly exchanged 10 ℛℳ to 1 DM.
It's hard though to make a direct relation between an investment in ℳ of 1920 and the proceeds in DM in 1950; one would need to know the exact share prices from that time.