That is a very interesting question OP. I take it you are assuming that every single state and civilisation that existed made it an explicit goal to reach the moon.
First of all humans would waste millennia stuck on basic steps or going down the wrong path. At all points in history all communities wanted to get better tools, and would devote great attention to acquiring them. And yet it took from the start of the bronze age in 3300 BCE, when it was discovered that tin could be a non-toxic supplement to turn copper into bronze, until 1200 BCE, to discover the superior metal of iron. It would take thousands of years until humans figured out some important basics: to forge good materials, to write down knowledge about the mysterious Luna rather than pass it by word of mouth, and to cooperate instead of massacring each other out of existence, as the more people there are the more complex the civilisation can grow and more brains can work on the problem.
Humans would undoubtedly attempt to reach the heavens by flying to them like birds. We know such wing-flapping machines are still unbuildable. Perhaps they would figure out gliders and launch them from catapults, but to no avail. Flying by hydrogen or hot air balloons would only be figured out after a study of chemistry, that would come after centuries of alchemical pursuit of gold, something that would happen sooner with more advanced civilisation.
The most important thing the horse-riding yokels would have to figure out is to study the world through carefully compared empirical observation rather than pure philosophical conjecture. Experimentally they will find pressure decreases with height, as does the effectiveness of airfoils and aerostats, and reaches 0 in space; Luna is in vacuum and a study of vacuum would commence, perhaps recreating the works of Goddard, testing the reaction force of rockets in vacuum, and they could start with ancient chinese firework rockets and work their way to liquid propellants.
cont.
