I think rocketry progressed about as fast as it could post WWII. America went full tilt to develop IRBMs and ICBMs. Vanguard evolved from Viking, which did not suffer undue restrictions in its development. Redstone was Von Braun's rocket and a direct successor to the V-2. One could argue that it took a few years for the imported Germans to set up shop in America--on the other hand, they had access to more resources in their new country.
Artificial satellites are a side-effect, not the prize. Of the main early boosters that lofted orbital missions, only one had been designed from scratch for that purpose--Vanguard, and that one isn't going to fly any faster.
The others:
Juno I (Jupiter-C): Redstone IRBM with Sergeant solid rockets on top
Juno II: Jupiter IRBM with Sergeant solid rockets on top
Delta: Thor IRBM with Vanguard second-stage on top
Atlas: ICBM
Now, Project Orbiter could fly in 1956. It might even fly as early as 1955. There are political reasons why it did not, however.