There is almost 5 months between OTL Sputnik-1 and Vanguard-1 so it's possible that given a sufficient delay to Sputnik Vanguard could get there first but I would wonder if being 'beaten' in an unannounced 'race' would not lead the Soviets to simply go to their 'default' mode of "we weren't racing in the first place" as they did for the Moon? And frankly if the US DOES get there first there would be little notice, (we fully expected to be first which is why Sputnik and then Gagarin was so much of a panic) and frankly little support for an expanded program from that point. ARPA came about because of Sputnik and very rapidly due to Eisenhower's dislike of the idea of a "military" Space Race, (and Johnson's need to make political hay AND siphon some funding towards the South and Texas in particular) NASA followed in order to 'address' that shame/panic. If the US goes first it is very likely one or either of those 'responses' don't come about.
Well, that would be the point. The whole idea of a Vanguard-first scenario is to pop the bubble of the Space Race before it even began, so things just go...boring. But honestly nixonshead's already done it perfectly well with
Kolyma's Shadow, so I'm not too inclined to try this scenario.
You 'guesstimate' a couple of billion dollars to move manned operations from LEO to Cis-Lunar space but really the very conservative original concept of Apollo, (without the Kennedy less-than-a-decade deadline and budget) was to meet both LEO and Cis-Lunar goals with only 'some' modification within a budget of about that amount.
No, I guesstimate that it will be between several hundred million and a few billion dollars (in 1960s money) to do that. Sure, the projections might have been that it would cost a lot less than that, but the projections
always say that it will cost a lot less than it actually ends up doing. Even with a cut down SM so that the CSM doesn't weigh as much, the Saturn IB just doesn't have the oomph to kick a CSM around the Moon--it could only put around 4-5 tonnes on a trans-lunar trajectory, which is less than the CM by itself. Sure, there might be a lighter CM, but 4-5 tonnes is really marginal for a crewed spacecraft and not really likely for any alternate Apollo design. You're gonna need to do
something expensive to go from there to cislunar flights: New launch vehicle, modifying the Saturn IB for boosters, on-orbit refueling capability. I just don't see Congress ponying up the money for that if the Space Race is perceived to have been won, just the same way that Congress has been cool on all proposals for space exploration beyond Earth orbit since Apollo IOTL.
And then there's the early planning for a 'space tug' to move satellites around that would be reusable and would be refurbished on-orbit. Currently a significant amount of money is spent on satellites to ensure backup and redundant systems since once on-orbit it can't be serviced or repaired. Early planning assumed that servicing and repair would be a requirement and while vacuum tubes gave way to solid state electronics which reduced the need if the requirement had been built into the overall system itself...
I think this is a very hard thing to get around, because you're not, realistically, going to have a space tug available until well after people have started going to high-cost engineering to keep satellites alive. Early launch vehicles aren't going to be capable of launching something like that, and by the time you get later launch vehicles satellite builders are already focused on reliability, not easy repair. Not to mention that a reusable space tug probably doesn't make all that much sense without a reusable launch vehicle to make servicing it cheaper than buying a new stage. It's notable that already in 1970-1971 NASA's proposals that satellites be redesigned for cost instead of reliability attracted almost no attention from anyone actually building satellites. Not to mention that JPL and Ames, at least, are going to have to be spending tons of money on payloads anyway; you can't get space probes back from the Moon, let alone Mars or Jupiter...
If the flight rate is higher, (as NASA and the Air Force originally planned it to be) then it makes sense they want to reduce the cost. Or course we already are aware there's two ways to do that; Reusability and/or dirt-cheap rockets and increased flight rates.
It's more the other way around: The Saturn IB/Apollo combination, and Saturn IB in general, is so fantastically expensive that they need to find ways to get the cost down to enable the flight rates that they want.
The former was assumed to be the obvious path forward but I'll point out that the Air Force had already shown that with any 'realistic' flight rate projection "mass-produced" expendable rockets could be shown to give reusable rockets a run for their money. In fact that 'argument' was in place in the mid-60s as both NASA and the Air Force put the Saturn-1/1B and Titan-III head-to-head in economic terms. Under the assumed circumstances the Saturn-1/1B wouldn't lose so much in comparison as it did OTL because it WOULD be flying more and remain in production but in a very general sense the Titan-III would still have an edge.
Why do you assume that the Saturn I/IB would be flying so much more than IOTL? NASA has a much smaller budget without the Apollo program (of OTL), so they're not launching more missions...more robot missions, sure, but those are mostly going up on Atlas-Centaur, not Saturn IB.
And frankly...despite all the arguments in favor of cheap expendables...the idea of reuse being the way forward is so baked in to the assumptions of everyone involved (literally predating the first orbital rockets!) that I don't think they're going to give up on it until they're
forced to, as they were IOTL (first with the failure of the Phase B Shuttle to get approved, then the failure of Shuttle itself to be economical).
It would also depend on if NASA had gotten around to establishing reuse for the Saturn-1/1B as was researched but no implemented OTL. In general it would not be that hard to begin such operations from early on and would allow a more effective argument with obvious evidence which OTL lacked. Under such circumstances the Titan-III economics would look a bit weaker but to be frank the military has always had the National Defense argument to fall back on and they'd use it very specifically in this case. Another point though is by utilizing the Saturn S-1/1B design the way is open to using SRBs for performance enhancement of the basic launch vehicle which the Air Force is already showing the way with the Titan-III and frankly NASA would have to embrace to continue to support future operations.
I'm highly skeptical that the S-IB reuse plans would have succeeded. The evidence of later attempts to try to reuse stages through parachute recovery is pretty poor. I'm not saying that the H-1s would have melted in the sea water, but rather that they'd probably have problems with parachute deployment, stage tip-over on water impact, things of that sort. Solvable, perhaps, but the kind of problems that add up and add up until you start wondering why you don't just go for the flyback stage and get something that will be better, anyway.
"Full-reuse" (pretty much flyback with the mindset given) would require a complete reworking/redesign of the S-1 stage so it would be arguable that NASA might simply 'move-on' to the orbiter/orbital stages from this point.
Yes, I'm aware of that. The idea is that they build a reusable first stage since that saves as much, if not more, cost as a reusable upper stage while being much easier (i.e. cheaper) to build: it doesn't need an elaborate TPS because it never reaches orbital velocities, the weight doesn't impact payload performance as much, it's much easier to test, etc. etc. So they can afford to do
that first, then, in theory, use those savings to pay for the reusable second stage/orbiter vehicle, or at least justify the second stage/orbiter budget to Congress.
We should keep in mind that historically what NASA says it 'wants' as requirements and what it actually 'needs' are often not the same thing. For example the Martin 410 Apollo design was in fact very much addressing what NASAs requirements for "Apollo" were as the NAA design was more geared to its 'wants', or more specifically Faget's "wants". A more modern example was the outcome of the "Orbital Spaceplane Program" of the late 90s where NASA insisted they "wanted" a Spaceplane but examination of their actual "needs" showed that what they were actually looking for was an advanced capsule design. (And again as OTL history showed NASA ended up picking the 'winner' by who they PLANNED on winning rather than the design)
The Martin 410 was essentially the same as the Apollo that actually flew. The only significant difference was that it had a lifting CM instead of a capsule CM, which makes no difference in terms of the feasibility of reuse. Indeed, the CM design it was using wasn't actually capable of runway landings anyway, and needed parachutes and a retrorocket for land landings. It would have been just as feasible to reuse the actual Apollo CM as one of these capsules, a la Dragon, if anyone had cared to do so.
Besides, in 1961-1962 understanding of lifting bodies and similar lifting designs was in its infancy, whereas blunt-body capsules were pretty well understood thanks to Mercury and the military ICBM programs. Thus, for the purpose of exploring how to live and work in space (which I imagine is going to be Apollo's mission
sans Moon target; figuring out what useful tasks astronauts might do in space and how they might do them, the way that Mercury showed that astronauts
could live in space) a capsule design makes more sense while NASA researches lifting bodies and lifting reentries (via X-15), with any lifting design (i.e., in the minds of engineers at the time, any
reusable designs) deferred until the post-Apollo program.