We could, technically, make one from wood. The problem with wood is that it can deteriorate if you're not careful, and wear away which of course means that the precise measurements that are necessary can become altered. Now, if we maintain the wood and are careful with it, it can still work.
We'll just use metal moving parts so they don't strip as easily, that'll mean we can use far less metal. And the hardest part of a sextant, really, is the math and precision. The rest of it is basic building.
And Panem sounds terrible; no offense, just, the iron curtain mentality is a bit on the reviling side for me.