Soviets taken humans and dogs outside, with less budget, techology and time than spaceX. Some of their designs still are in use (Soyuz, Energia rockets).
Nasa never developed nothing completely "inside", always was contract-driven. So State owned v/s private in United states, is quite nonsense. NASA served as a coordinator and financial support for many technological developments carried by universities, private companies, from US and another countries. Without it, probably some technologies never reached commercial/industrial grade.