Supersonic flight or rocketry for at least at 1941.
If you want more advanced rocketry just give
Robert Goddard more funding and resources pre-war, along with Tsiolkovsky and Oberth he's considered one of the fathers of the field.
Cheap/Good Solid Rocket Fuel: The combination of asphalt as an appropriate binding agent with potassium perchlorate as its oxidizer could have beend discovered even before the 20th century. Also nice for JATO.
For liquid rocket fuel high test peroxide (HTP) is another good option since it's fairly easy to store and use in comparison to some of the other more volatile fuels of the period whilst it decomposes into oxygen and steam of a high temperature if it comes into contact with a catalyst. All it takes is for someone to make the discovery that silver plated nickel mesh makes for a good catalyst to pump the HTP through and turn it into steam and oxygen and you can leave it as that monopropellant or pump kerosene into the chamber where its ignited by the heat of the steam to increase the thrust as a bipropellant. Post-war the British produced a Rocket-Assisted Take Off (RATO) booster in the
de Havilland Sprite which used just HTP as a monopropellant and developed it into the Super Sprite which added kerosene as a bipropellant.
Considering that they used cordite rockets to test their early proximity fuze prototypes until they could develop them to resist the forces exerted on them by being fired out of a gun I've wondered off and on about the Allies developing a first generation surface-to-air missile. We're talking fixed launch sites and probably only useful against large aircraft like bombers but HTP/kerosene provides the propellant, Goddard had done successful work on three-axis control and steerable thrust to control its flight, and the fuselage isn't too complex. Radar to track the target and guidance could be either basic line-of-sight beam riding guidance (LOSBR) or stick a small beacon on the missile to track it and use command guidance in the form of semi-manual command to line-of-sight (SMCLOS) where the controller guides the missile to intercept the target or semi-automatic command to line-of-sight (SACLOS) when it's handed off to an analogue computer to guide the missile close to the target where the proximity fuze detonates it.