If by "end goal" you mean, "knew they were working to build a nuclear weapon" — there's no hard and fast number. My sense of it, having studied this topic closely and thought about this very question specifically, is that it was on the order of thousands (as opposed to hundreds or tens of thousands), if you tally up the people who needed to know that to do their jobs at the various sites. (There were 125,000 workers simultaneously employed at its peak but it is worth noting that the total number of people who worked on the project is more like 500,000.) Which is to say, I find 1-9% to be in the likely range, probably around 1-2%.

The vast majority of the employment on the project was for construction and facility operations, and they would not have been told what their end goals were at all. At the production sites, only some technical consultants and some very high-level people would have known. The places where you would have relatively large numbers of people who knew the purpose would have been Berkeley, Chicago, and Los Alamos, and even at those sites it was fairly compartmentalized.