Don't even get me started on airplanes though - there was only 66 years between the first airplane (Wright Flyer in 1903) and the moon landing (1969).
Disclaimer: that's of course a cool anecdote on the surface, but rockets have been around since the 13th century so they're two mostly different technologies.
Key development for flight: Wings which carry the plane. First planes didn't even have an engine (besides human)
Key development for rockets: Strong powerful engines to escape gravity. Aerodynamics matter relatively little, mostly for heat control.
I don't know how related the development of jet engines and rocket engines was. Of course things like the Space Shuttle, which has some airplane-like aerodynamic steering tie both together ...
We're playing a bit fast and loose with our phrasing here if we want to split hairs about the development of these technologies.
Powered, navigable, human flight existed before the development of wings.
The early rockets mentioned above weren't for human flight, nor for spaceflight. Rockets were developed to be terrestrial weapons, not to propel humans.
Rocket engines and turbine engines are both a type of jet engine. These engine technologies themselves weren't developed together because one was developed to make airplanes go higher and faster, and the other was developed to stab people with arrows better. If what we're really talking about is "human flight", then rockets and turbine engines were both used to propel humans on airplanes before anyone started considering spaceflight.
And then when humans did consider spaceflight, humans were developing space planes and tubular orbital rockets at the exact same time. The space shuttle was far from the first plane to operate at heights where the control surfaces no longer work. The X15 actually flew 2 years before Vostok 1.
The people developing human flight were always interested in going faster and higher. The technologies they experimented with were intermixed the whole time.
Disclaimer: that's of course a cool anecdote on the surface, but rockets have been around since the 13th century so they're two mostly different technologies.