That could be one approach; another would be a lunar orbital
Are you proposing the guidance system be back on Earth for lunar descent and ascent stages of the mission?
That could be one approach; another would be a lunar orbital station large enough to provide real time data to a landing craft.
Again, my estimate was (ROM, SWAG, etc.) 10 years of concentrated Manhattan Project level of effort as an option in comparison to 25 years of intermittant effort (1945-70) that ended with Project Apollo.
Keeping things as simple as possible, with a 1945 kickoff (say, a Anglo-American vs. Nazi Germany-occupied Europe cold war) I could see a basic building block approach around multiple RP-1/LH2 analogues of Atlas-Centaur or Titan-Centaur (with an RP-1-fuelled Titan, rather than the exotics), with the immediate need for LEO reconaissance. Lunar exploration is essentially the cover for the recon program.
Here's a (very back of the envelope) timeline:
1945: Manhattan II kicks-off;
1950: LEO Manned Orbiting Lab/KH level recon capabilities, but using HSF rather than automated systems;
1955: Orbital workshop to repair and sustain constellations of multiple MOLs; manned lunar fly-bys (free return) as cover
1960: Lunar orbital station as base for descent/ascent; first lunar landing.
That's 15 years of concentrated effort, as opposed to 25 years of intermittant effort historically; the basic launch vehicle will be substantially smaller than any of the Saturn variants, but there would be heavy reliance on rendezvous and both earth orbital and lunar orbital staitons, with what amounts to the classic concept of a "three legged" trip - ascent to and descent from LEO in a roughly Titan IV-Big Gemini type vehicle to a modular analogue of Skylab; department from the LEO station in a "flying dutchman" type EDS (clustered Centaurs?) for the Earth-Moon leg, to rendezvous with a lunar-orbital MOL-equivalent; department from the lunar orbital station in a reusable descent-ascent module roughly equivalent to a LM....
It wouldn't be cheap, but technically it would be doable, I think; multiple rendezvous is not simple, but it is fairly robust and with active piloting(which I think would be necessary given the state of electronics in the 1950s), it would actually be necessary to focus on HSF.
My two megabucks, anyway.
Best,