I mean isn't it absolutely crazy how a destitute nation could have access to such great minds as to have made the Enigma, Tiger tank, V3 rocket and stermgever?
It seems to me that you assume that if there is hunger and some political chaos that all the institutions stop functioning? Germany before WWI was one of the most advanced countries on the planet, they won the most Nobel prices in the sciences up to that point. WWI was 4 years and after it was over the scientists or institutions didn't just disappear.
They might have been destitute right after the war but they still had one of the biggest economies in the world plus the institutional memory and tradition in the sciences, engineering didn't vanish.
http://www.worldeconomics.com/Data/MadisonHistoricalGDP/Madison%20Historical%20GDP%20Data.efp
I hosted the spreadsheet on my Google docs if that is easier:
https://docs.google.com/spreadsheets/d/1c6VaKFh7znO4RT_FBJxQcQLepehkf_4ymwZclpnx-M8/edit?usp=sharing
There GDP took hits in those years but they never got below France there level and overtook England in the inter war period. GDP is a flawed way to look at the economy but it's useful to illustrate my point that they weren't as destitute as you might have thought.
Leading up to World War 1 Germany looked like an academic and industrial juggernaut. Their universities were numerous and the best in the world. Their factories produced more and better goods than anyone else. They appeared to be accelerating as well because foreign leaders were quite worried about the rise of Germany into a continental juggernaut. David Fromkin goes into the specifics of their ascension and the perceptions of it from elsewhere in the beginning of "Europe's Last Summer".
Then despite the heavy cost of the war there was little destruction in Germany proper outside of malnutrition and some starvation as a result of the Allied blockade. This meant that that superiority in academics and manufacturing largely remained intact. In the last years of the war and until 1924 the German economy was in shambles but there was a golden period until 1929 when everyone tanked. Germany then came out of the Depression a little earlier than most countries so they really had favorable conditions between the wars to maintain their advanced status.
hi! You may be interested in these posts
general background
the run-up to WWII
Was Germany more advanced technologically than the allies during WWII? How did they progress faster?
Prior to WWII, why were German scientists so good at what they did?
Why was Germany so far ahead technologically prior and during World War II?
Was Germany more advanced technologically than the allies during WWII? How did they progress faster?
How were the Germans able to field such a large and technologically advanced army during WW2?
Any information of the Investment in public education system under Bismarck?
Enigma was invented in WWI by Arthur Scherbius, a person who died before WWII even broke out.
Ferdinand Porsche, designer of the Tiger tank, was born in 1875 and died in 1951.
Hugo Schmeisser, inventor of Stg44, 1884 and died in 1953.
Einstein, famous German Scientist and nobel prize winner, was born in 1879 and died in 1955.
All of these people were born before WWI. All would have been post-university age by the outbreak of WWI (i.e. at least 25+. Einstein is an interesting case there). So unless they died in WWI, or fled to another country (as Einstein did), all would have been able to contribute to WWII's technological efforts. It's not as if they stopped existing on the outbreak of WWII!
Wernher von Braun, person behind the V2 rocket (I assume you meant V2 rocket?) and later main initial component of NASA's rocket program, was born in 1912. He got his PhD in 1934 -- and so is relevant to your question. For his teachers: See above. Other "old" people still alive before the outbreak of WWII. For his materials: See /u/Slashenbash's comment about GDP.