You’re incorrect in terms of the space program. The US and Great Britain etc where very interested in rocketry and therefore spending significant sums before Sputnik. Which is how the US was able to launch a satellite in 1958 a year after Sputnik.
You don’t go from knowing nothing about rockets to launching a satellite in a year.
Further, the US slowed down but didn’t abandon its manned space program. It was spending a frankly crazy amount of money on a publicly stunt to get people to the moon, but we’ve continued to invest in the space program over the long term. Actually going past the moon requires long term habitation in space thus the interest in space stations.
everybody was interested in rocketry ever since V2s demonstrated that a good rocket made a good weapon.
The US wasnt particularly interested in space exploration unless the USSR did it first though.
Just like the UK wasnt interested in setting up an NHS until it became glaringly evident how well the soviet NHS (also called the NHS) worked and the US won't set one up even though ~70% of the population want one.
You don’t go from knowing nothing about rockets to launching a satellite in a year.
Further, the US slowed down but didn’t abandon its manned space program. It was spending a frankly crazy amount of money on a publicly stunt to get people to the moon, but we’ve continued to invest in the space program over the long term. Actually going past the moon requires long term habitation in space thus the interest in space stations.