Just some examples: take a string, don't bother to measure it, just any length between 1 and two meters or so would do. Take a pencil (or a piece of charcoal if you really want to go native) and a smooth branch. Stick the branch in the ground, tie the string around it so that it can slide with little friction and put the pencil in a loop of string on the other side. Now use this to create a circle. You started off with very rough elements not specifically sized for any purpose and ended up with a high precision representation of a mathematical concept.

Another: take a bunch of roughly cast metal balls. Put them on a sieve and let it vibrate until the balls have all passed through the holes in the sieve. Behold: metal spheres, so precise that you probably can't really measure the degree to which they are not spherical without resorting to instruments that you're not supposed to have in this scenario. Then sort by weight (which is a proxy for size). Now you can make ball bearings.

Yet another example: you can cut a lens for a telescope to within ridiculous precision using very primitive methods (https://www.instructables.com/Grind-and-Polish-a-DobsonianNe... ).

Put another way: it is always possible to increase your precision as long as you don't particularly care about absolutes or temperature effects.