I suspect the better POD for getting a generation or so of widespread use of ramjets for manned aircraft would be to go back in time somewhat rather than avoid WWII. I disagree that avoiding the war would delay turbojets a whole lot; maybe half a decade. But the desire for thrust at speeds beyond what a practical propeller could sustain was there; the evolution of the turbosupercharger, in service to providing more power in piston engines and extending their high-power ceiling (to take advantage of thinner air allowing higher cruise speeds at a given L/D ratio--provided one could get the power, and this evolution unfortunately does nothing to eliminate the problem of high drag as prop tips exceed Mach 1--rather worsens it in fact) lays the groundwork for practical turbojet components, turbine and compressor both. Lockheed designers were working on layouts for jet planes before they had an actual turbojet ready to hand; they were that confident one would be coming along shortly. I don't think the run-up to war had tremendous bearing on this foresight of theirs, nor on Soviet designers who also were well on the way to turbojets, although undoubtably it had some relevance for the cash flow of the parent company to afford diverting some funds on this blue-sky stuff (substitute appropriate alt-"funding" and "design bureau" for money and company in the Soviet Union of course). Both Lockheed and the air/rocket minded Soviets were forward-looking and even with leaner funding would have puttered along with these, even on the back burner. So the war certainly did enhance Ohain's prospects in Germany and allowed the British Air Ministry to belatedly catch up with delays caused by their own muddle-headedness. But with a somewhat less obstructionist AM in Britain (probably ASB, I know!


) I suspect an ATl peacetime Britain of the late 30s could and would have pioneered turbojets well before 1945, if only they listened to Whittle. If not, an ATL non-Nazi German regime would probably have still funded Ohain.
So the issue with ramjets is that for human-bearing planes, that have to take off and land repeatedly, they suck compared to even rather primitive turbojets. One basically has to be working before turbojets are a pragmatic thing to put on the shelf.
Combined with some sort of alternative thruster--be it propeller, rocket, or something else such as a pulsejet (a poor alternative, just mentioning it for example) I suspect a workable ramjet could have been made long before a turbine and compressor combination was practical. The chief barrier, aside from the matter of how to reach ramming speed in the first place, would be the temperature of the combustion chamber. (Also other issues to be sure--flameholders for jet engines are a challenge that needs to be met for instance).
But I suspect liquid-fueled rockets could have been developed, in some forms anyway, some decades before they were. I'm going to advocate for high-test pure hydrogen peroxide as oxidant and possible monopropellant. And suggest that alternate nozzles might vent into the duct of the ramjet itself; to an extent the stream of a rocket exhaust plume can induce air flow and augment ram pressurization, while if a peroxide rocket burns fuel-lean, or with no fuel at all, it releases heat and also free oxygen into the ram combustion region.
So, fire the rocket for takeoff roll and initial climb and acceleration; at a speed below that the ramjet would need to start effectively thrusting by itself divert the rocket blast into alternate nozzles within the ramjet duct to increase ramming pressure and temperature, and augment the oxygen available, so as to ignite the ramjet a bit early. Keep this up but throttle back on fuel for the rocket as the plane gains speed, so there is less induced compression going on but more oxygen release to burn extra fuel thus raising thrust hence acceleration until one has reached full ramming speed.
For purposes of high-altitude combat, the peroxide can also be injected as sort of an afterburner in reverse; enhancing the oxygen to enable heavier fuel burn; along with the water mass released and the heat released by the peroxide decaying this gives a burst of thrust for a speed surge that can either power additional climb or be used as speed in combat maneuvering.
Ramjets can work at subsonic speeds but they are of poor efficiency there, guzzling fuel at a high rate for a given thrust. But once sustainable ramming speeds are attained, the rocket can be shut down, so we aren't guzzling the still greater mass of oxidant even faster. One reason I like peroxide is that the fuel for the rocket is the same stuff as for the ramjet. Another is that hydrogen peroxide reacts with fuels at a very high ratio of oxidant mass to fuel mass, since over half the mass of the peroxide is released as a water molecule, which serves to augment the mass flow--at the cost of diluting the oxygen-fuel reaction to be sure, thus lowering the specific impulse--but raising the thrust per unit of fuel. And also the temperature. Somewhat more energy is released than with the same mass of fuel and pure oxygen because the degeneration of the peroxide releases some extra heat; the doubling of product molecules (due to each oxygen atom coming attached to a water molecule) reduces the exhaust speed by some 30 percent, but halves the temperature compared to a pure oxygen reaction so at a given state of the art in combustion chamber metallurgy a higher rate of fuel consumption hence power can be attained--or alternatively at a more conservative rate the materials can better endure for longer service life.
The main mission for such an aircraft would have to be point defense interceptors, designed to scramble on little warning, rapidly climb to high altitude and then zoom and boom on their targets. For this mission little range or endurance is required.
I'd think anyone working on such a project would have in mind supersonic operations; at supersonic speeds the ramjet is more efficient. In the early 1930s very little was understood about supersonic operations so whoever does this would have to invest years in expensive flight tests, one hopes largely of radio-controlled models, to feed into exhaustive theoretical investigations. They'd learn all sorts of surprising things, like control reversal, and to be really successful would have to hit on the area rule, either theoretically or empirically, so there would be a large time gap between development of the engine combo and practical deployment of workable weapons systems.
Trying to go for really high Mach numbers would be tough for many reasons, even though the temptation would be strong due to ramjet efficiencies improving as one approaches Mach 3 (or perhaps even higher). OTOH it is also nasty trying to operate at speeds very close to Mach 1; the transonic region is to be avoided. So I suspect early-generation versions of these things have to operate around Mach 1.2-1.6 or so.
The plane would take off on rocket thrust, and both climb for altitude while also accelerating for speed; high thrust is favored for the rocket since it cuts down the time to approach Mach 1. I suspect it would be helpful to take advantage of what ramjet thrust one can get below Mach 1 but there won't be much below 2/3 or so the speed of sound. Then as one approaches Mach 1, go into a steep dive with all the thrust one can muster as well, to punch through the sound barrier and reach Mach 1.25 or so as quickly as possible, then pull out of the dive, ramming at near sea level supersonically and once again rise to high altitudes on high ramjet thrust, maintained pretty level by the rising speed offsetting falling atmospheric density up to very high altitudes. By then in a combat situation ground observers and possibly radars (remember, mid-1930s tech, so possibly no radars) have helped locate the target to be intercepted, the plane dives down "tally-ho!" and seeks to shoot it down. It will burn up fuel quickly and so have to glide to a landing, but a small reserve of fuel and larger one of peroxide can supply thrust for the actual landing itself and possibly a go-around capability.
With fairly mediocre chamber pressures and design features, I'd figure peroxide/kerosene (or other hydrocarbon, but kerosene is probably the right stuff) rockets can get an isp of 220-240, maybe more but let's go with about 230, exhaust speed of 2300 m/sec. With a mediocre thrust/weight ratio of say 24, on a 12 ton airplane (ginormous for a 1930s era fighter to be sure) a thrust of half its weight would come from a one ton rocket engine installation. I doubt the ramjet would mass a lot more, considering its simplicity, being basically a duct with some flameholders installed. A 60 kilonewton thrust implies consumption of 26 kilograms of propellant per second, most of which would be hydrogen peroxide, in about a 7 to one ratio, so just 3.25 kg of kerosene and thus a ton of peroxide would be used up in 44 seconds. Note though that if the total "engine" installation is just 2 tons, and by rule of thumb engines ought to be about 1/4 the total mass, we have that ton to play with "for free" before the peroxide starts seriously robbing us of other useful weights. Within 20 seconds or so we should reach takeoff speeds (assuming 100 m/sec, or a third the speed of sound at sea level, some 200 knots(!) is takeoff) and rise to half a kilometer or more in the next half-minute. 2 tons of peroxide should be adequate to get the plane cruising at say Mach 1.333, burning kerosene at say 3 kg/hour-kg thrust. Needing maybe a thrust/weight ratio of 1/5, so two tons of thrust at that point, would consume 6 tons an hour, so endurance would be only half an hour or so. At that speed the plane could travel up to 300 nautical miles, so an alternate use might be to courier top-secret documents not trusted to electronic transmission in 5-degree bunny hops involving frequent landings, refuelings and takeoffs; I daresay the thing would spend more time in approach, landing, refueling and climbing again than at cruise speeds so perhaps it would not compete with fast prop planes that can keep flying steadily for hours.
Once someone develops practical turbojets, they would eclipse these things for the low supersonic interception mission, but on the other hand at an OTL 1945 state of the art, experience with such ram-rockets would allow for immediate development of higher-Mach craft capable of cruising an hour or so at say Mach 3; they'd take the courier role, probably be suitable for an early version of SR-71 type surveillance missions and stand ready to serve as low-hypersonic interceptors, long before anyone can develop turbojet engines to enable these missions. When such turbojets do exist the ramjets would finally be obsolete for manned missions I suppose.
So a window of opportunity exists between 1940 and 1960, benchmarked to OTL possibilities, for such a hybrid rocket-ramjet to find operational niches. But 1940 assumes that for more than half a decade before someone has been investing in developing a practical version by that target date; starting then instead is too late.