The long answer would probably be that access to these resources would be gated through pay-per-use, instead of a distributed taxation system. Of course for convenience you might end up with a structured way of purchasing a group of resources and it might even look like a roundabout way of taxation, although libertarians might argue that taxation is the roundabout way.
Or they might give a different answer, there are different schools of libertarianism!
* not a libertarian, but interested in niche political ideologies
The libertarian ideal is voluntary payment for services. Don't want to pay for fire protection? You don't have to; the flip side of the bargain is that if you haven't chosen to pay for fire protection, the fire company is under no obligation to put your house out if it does catch on fire. The choice is yours, but you have to be wiling to accept the consequences of your choice as well.
Note that I have not studied the various flavors of libertarian philosophy, so some of them might well disagree with what I just said. But the voluntary/involuntary thing is pretty important to libertarians as far as I know, so it's definitely worth mentioning here.
What's described is basically just a regressive tax. It doesn't sound very libertarian to me.
Or pollution, are small amounts ok, as long as nobody can prove they are damaged? What if damage takes a generation, or only appears if lots of people are doing it? Diluting away the crap from burning a little oil is easy, when the whole world is doing it everybody is hurt.
I want to ask you since I'm curious, the state simply declared ownership over territory and resources (and in some cases used violence to uphold it), why should you recognise any power in the state's part to do so? Likely many of the same justifications can apply to individuals as well.