You wouldn't need coal. If you can make a fire, charcoal is easily produced from wood.
Making forges and blast furnaces isn't too difficult. To build one, pile up dirt or clay walls to form a bathtub like structure. Make sure you have holes at the base so air from your bellows can make it though. Construct a fire in the tub and pile on alternating layers of charcoal and iron ore. Keep pumping on the bellows for the next few days until the the charcoal burns up. Your iron ore should now have turned into pieces of high carbon steel, perfect for making any tool from ploughs to blades.
You might be able to find iron ore as dark colored sand in stream beds. I don't know where you would find copper or zinc.
Once you have steel, everything follows. If society knows about existence of a technology, reproducing it shouldn't be difficult. The hardest part about progress is inventing brand new things.
If you are interested in learning how to make machine tools from very simple materials, look up the Gingery series on making a complete metalshop from scrap: