The Saturn V of Apollo 11 was 111 meters in height. So yeah, in 1912, before the first tank even was invented, he was off by a factor of <4 (< two doublings).
Multi-stage rocketry made everything possible. The era of multistage rocketry started in the late 1940s to early 1950s.
The power of multistage space vehicles is the ability to dump weight when every stage is lost. You may recall the outrage that only a minute portion of the Saturn V ever comes back to earth, and how *wasteful* this is, which was probably a Major factor in Apollo cancellation - to take a time-out for technology improvements, hence the reusable shuttle program. This was the zeitgeist at that time. Avoid the terrible waste.
Multistage rocketry was the brainchild of Hans Oberth, Von Braun's nazi boss, see first paragraph here:
Oberth never moved to the US with WVB at the end of WW2, he stayed in Europe and was never part of the US space program but clearly WVB caught on to the concept.
Even if WVB has written that during or immediately after WW2, which was techologically very different from before WW2, which was very different in turn from before WW1, how many doublings does the amount of PC-addressable RAM increase In just 4-5 years? Moore's law says computing power doubles very 18 months.