The real issue isn't so much that the technology would not exist, rather the social and economic conditions which would allow for space travel might never exist outside of the Enlightenment.
Consider that Hero of Alexandria published a book in the first century AD which described simple steam and atmospheric engines, and the Romans certainly knew about things like cranks and what we would describe as clockwork. Despite all this, no "industrial revolution" took place in ancient Rome. It didn't happen in the Hanse, Renaissance Italy or Elizabethan England either, despite having many or even most of what we consider critical factors for creating an industrial revolution. Ancient or Medieval China had many of the same factors (and as a bonus actually invented black powder and rockets), yet they never got there either.
So we have a combination of a multitude of factors, including the philosophical recognition of Space as a different environment as far back as the Ancient Greeks, but no one ever puts all of these things together. There are a multitude of theories as to why, but most seem to be based on the various social and cultural factors in play at the time. The Ancient Greeks and Romans, for example, looked on what we call science and invention as the playthings of philosophers rather than a serious business with immediate and long term payoffs to the adopters and inventors of devices and machines. (Most of Hero's devices were described as toys or "special effects" used to make temples impressive or deliver a satisfying ending to a play).
Things get even worse in other parts of the world. When Cortez was driven out of Tenochtitlan, he went around gathering up charcoal, volcanic sulphur and saltpetre, elements which had existed in abundance in the region for centuries, and made gunpowder and built cannon to retake the city. The Aztecs had no idea of what happened to them, despite having all these materials at hand.
So the various pieces have been sitting there in plain sight, but the "mental" tools for putting them together simply did not exist. Should our own civilization end, it is difficult to imagine the set of circumstances which might lead to a new spacefaring civilization arising from the ruins.