Resources are an important aspect of the game. Their basic deposits deplete fast, so first you should focus on unlocking mining buildings. They will enable you to mine resources from places where simple human wouldn't be enough. They also enable you to spare some workers. In addition to that, these deposits are larger.
Carbon can be mined even without technology - all you have to do is sent people to the deposit. However, keep in mind that it is ineffective and very risky. It is better to early develop technologies that unlock the possibility to construct mining buildings. They are definitely more efficient and they don't drastically wear out people.