Well, this is an “alternative history” question. If we hadn’t had WWII, or indeed the later cold war, would we have gone to the Moon in 1960s or earlier or later? I think it’s impossible to say. Once you start changing history, anything could happen - you can invent anything and say that might have happened, some genius who also has the resources to make it happen. This is a rather fun alternative history by an artist that has the first Moon landing on October 3rd 1725: Early Spaceflight: Tales From An Alternate History: Mr Timothy M Dooley. It’s rather sketchy and humorous in tone, but the basic idea I think is sound, that technology development did continue at a slow pace, say from the fifteenth to the eighteenth centuries, compared to the current pace of technology. What if something had happened to accelerate the pace of development of technology several centuries earlier?

However it would have happened eventually for sure. The ideas were there, and it’s hard to imagine a species possessing as much curiosity and a sense of adventure as humans not ever attempting to send something to the Moon.

So, it is just a question of whether WWII accelerated development or delayed it or made no difference. I think there is no way to know the answer to that. Indeed probably all of these are possible:

• Alternative histories with WWII, and humans get to the Moon before us.
• Alternative histories with WWII, and they get to the Moon after us
• Alternative histories without WWII, and they get there earlier
• Alternative histories without WWII, and they get there later.

However what you can say for sure is that the ingredients for a lunar misison were there already, in the form of quite detailed plans to go to the Moon before WWII. For instance the BIS Lunar Spaceship from 1938. More details with images here: The British Interplanetary Society at 80 Years

By then they already knew from the work of the early pioneers that a single stage to orbit rocket was impossible with the then current technology, as it would have to have a propellant to dry weight ratio of 100. They just didn’t have anything strong enough to achieve that back then. They could make something that was structurally possible with the technology of the day by making it a 4 stage rocket - but then the downside is that (again using the materials available back then) the final payload to orbit is 1/10,000 of the mass of the rocket. So 10,000 tons to send 1 ton into orbit. (I’m basing all this on the figures in the Centauri Dreams article).

By comparison the Saturn V at 2,950 metric tons delivered 140 tons to LEO, a ratio of 21:1. It has 2.65 km / sec exhaust velocity for the first stage and 4.21 km / sec for the second and third stages. Rocket and Spacecraft Propulsion. So it would be a rocket that weighted four times the mass of a Saturn V and delivered less than a hundredth of the mass to orbit. Possible in theory, they’d gone from impossible to theoretically possible, but not very practical.

Robert Godard in his much earlier 1919 A method of reaching extreme altitudes suggested a continuous motor. He illustrates it like this:

Goddard’s “Continuous rocket motor” on left.

With an exhaust speed of 7,000 feet per second (2.1336 km / sec), he worked out that he could achieve a 602:1 ratio - that’s for escape from the Earth’s gravitational field not just to LEO. He figured out that if he could send 13.82 pounds of flash powder to detonate on the shadowed part of the Moon it would be easily visible from Earth, and he reckoned that a rocket weighing 8 to 10 tons would be more than sufficient.

So - if by “reach the Moon” you mean just hitting it, and having evidence that you succeeded, before the days of portable radio transmitters well I wonder if someone with a lot of political power, or very wealthy, or a lot of charisma getting support for their ideas, could have done that already in the 1920s using Goddard’s ideas? I don’t know how feasible his design is, but he did do it on basis of practical rocketry experiments.

The BIS moon rocket was worked out as a continuous rocket, but with a larger exhaust velocity of getting on for 4 km / sec. And instead of lots of stages, it had five stages but each of the five lower stages would consist of 168 smaller rockets in a hexagonal cellular array. So it is the same “continuous rocket” idea basically - that you discard each of those tiny rockets when it is empty, so achieving something much closer to the 1 to 100 instead of the 1 to 10,000 mass ratio. It included a worked out design for a lunar soft landing and then return to Earth using 45 medium motors and 1200 smaller tubes in the final stage, discarding them continuously.

The design was human rated with a very early plan for a lunar spacesuit:

I don’t know how practical that is - this is a design that has never been developed into a working rocket, AFAIK - do say in comments if you know of anyone who has tried a cellular “continuous rocket” or any other form of continuous rocket in Goddard’s sense.

For more details, see The British Interplanetary Society at 80 Years. They also worked on many other ideas for spaceflight including inertial guidance, and gravity assist maneuvers See also the comments here

You can also ask, could Wernher von Braun have designed the V2 without the work of these earlier rocketry pioneers. The answer surely has to be No.

It’s a fun question, although I think we can never know the answer in any definitive way, and not sure it really has one.