Depends on how much people are focused on "the goal"
If people would just act on their instincts to survive, most of the humanity will die within the first year, and in the ensuing chaos almost certainly the people with knowledge (college professors, rocket scientists etc.) will be among the dead, without even a chance to write down what they know.
In 10-20 years, advanced stone-age societies will be set up, and some will even start working metal, and, most importantly, make recordings. This way, at least some of the knowledge will be saved. With that knowledge, stone-age societies would be able to make quick (probably within 100 years) progress to industrial era. After that, because scientific research has to be performed again, we are looking at another 100 years as the minimum before the space travel.
Any wars and epidemics will slow this process down, potentially to 1000 years overall, but not likely longer than that.
However, if "the goal" of reaching the Moon again is followed by everyone with religious zeal, things can be done much faster. College professors will be revered as holy men, they will be given as much tree bark or clay tablets to write as they need. Eager students would be competing to learn, even no Oxford or Harvard exist anymore. In case of wars, all scientists and their inventions should be spared.
In this society, after initial "stone age" phase, "space age" can be reached again in less than 100 years.
P.S. There is one important factor that is "reset depth". If all animal breeds and crop cultures are also reset (i.e. there will be no corn, no cattle, no chickens as we know them) then the society would be plunged much deeper and formation of stable states in 10-20 years would not be possible. This would turn the world into a prehistoric chaos, which, in my estimate, may last for thousands of years.