How do we know how much Uranium was in any given sample when it was deposited? Concerning "Uranium-series dating", also known as "Uranium-thorium dating". 
 Uranium is present in deposits, "typically at levels of between a few parts per billion and few parts per million by weight", according to the wikipedia article on the subject.

As an example, with carbon dating, the amount of carbon-14 originally present in any given sample is consistent with the amount of carbon-14 created by the activity of sunlight in the atmosphere.

How do we know how much uranium-234 was in any given sample of rock when it was created/deposited?
The chemistry of lead is very different from that of uranium and thorium. There are key kinds of rock that could not possibly have been formed with even the smallest amount of primordial lead. The lithophilic nature of uranium and thorium means that those same kinds of rock could easily have readily accepted primordial uranium or thorium.

Any lead in those kinds of rocks must necessarily be the result of decay of uranium or thorium after the rock formed.