Economic illiteracy: Germany would *not* be more advanced
I think the series is great as entertainment, but it is unfortunate that the writers seem to have a misguided notion of the likely outcome of Germany's authoritarian economic policies. It shows monorails in Berlin in a city that is implied to be prosperous and modern (monorails seem to be a common trope to indicate that) to a degree greater than US cities were in that year in the real world, more advanced high speed aircraft than we use today, and they talk about achieving goals like turning the Sahara desert green in ways we wouldn't realistically consider today (ignoring the debate over the propriety from an environmental perspective of doing so). The only area where the show suggests the real America developed more advanced technology by that year than the reich was the hydrogen bomb.
Some people who don't understand how economies function expected the former Soviet Union's centralized "command and control" system to be more prosperous and efficient than free markets, but of course reality proved otherwise. Free people have more incentive to create when they are working for their own benefit rather than that of an authoritarian state, whether the sort of attempted communism of the former USSR, or the sort of public-private partnership involved in the economic fascism of the National Socialist German Workers Party of the nazi reich. There is a misguided assumption that although the reich would infringe on personal freedom, that somehow a more command and control focused system would be able to more efficiently achieve goals.
It may be true that the ability to coercively direct resources towards 1 particular goal, e.g. a massive "build rocket planes" effort, might achieve that goal (since they keep throwing resources at it until they do), it would come at the expense of other aspects of the economy since governments aren't efficient. Historically private sector productivity improves over time, while governments tend to accumulate bloat. Economists and those who study organizational behavior see rational reasons for this due to differing incentives of the participants. Unfortunately studies show most of the public isn't economically illiterate, so it isn't surprising that writers might fall for the siren song of the "efficiency" of an authoritarian economic system under government control. Also, progress towards big goals tends to be sped up by progress elsewhere in the economy, which can suffer through centralized focus on particular narrow goals. For instance progress in computer technology sped up the development of advanced aircrafts.
The reich's extermination of its Jewish and other minority populations, and its many anti-intellectual attitudes where ideology was given priority over actual science, would have undermined their progress. There are always people interested in intellectual pursuits, even living within an authoritarian regime (there were intellectual advances in the USSR and China), but that sort of oppressive culture tends overall to inhibit the sort of experimentation and open minded thinking that is more likely to lead to progress (contrary to the portrayal of the more "free spirit" younger generation of Nicole et al that seem to be implying more experimentation even in the realm of personal freedom than seems likely to be tolerated in such a society, even among "elite" children). They might be paying lip service to that issue since they portray them as being behind where the actual US was in the development of a fusion bomb, unless they are merely viewing that as a minor historical accident rather than acknowledging a free society seems more likely to evolve science and technology faster overall.