Why is it impossible to build a machine that produce more energy than it uses?

First you need to learn what the words mean. Energy is not a physical unit. It is a philosophical concept and an accounting technique used to analyze mechanical and chemical exchanges. In nuclear physics it is defined as a wavelength of light, in biology it is a synonym for metabolism, and in public utilities they say energy when they mean connectivity. Anybody who uses the word in any other context does not know what he is talking about. What you want is work. Work is a force acting through a distance. What do you know that produces more work than it uses?

The Romans built an empire powered by muscle. The Dutch built an empire powered by wind. The English built an empire powered by coal. The Americans built an empire powered by oil. Not one of them made any great effort to develop any other source of power.