In particular try Italy and Spain, countries with many peasants circa 1900. Virtually identical trajectories.
The USSR, if around today, would have a population of 300 million. They were a superpower. Only large powers made it to space. It was certainly impressive, but also a natural result if you have a large portion of your economy devoted to military spending and missile research. The space program in both USA and USSR allowed for ICBM delivery of nuclear warheads, a crucial strategic goal.
Not that impressive if you consider population and vast, really vast amounts of land that have gigantic natural resources and lack of any real power blocking them from the east.
Basically with that base anyone could do it (I don't dispute that having a gun pointed at your and your family head wasn't mobilizing for scientists, but that's normal for authoritarian states).