New atoms form all the time, either through fusion or fission. The latter is happening right now all around you- either from potassium in plants breaking down,

New atoms form all the time, either through fusion or fission. The latter is happening right now all around you- either from potassium in plants breaking down, to radon gas that sept up from the ground, to carbon itself. All of these have unstable isotopes with half lives short enough to have at least a little activity near you. Given that constant change to the available combinations of sets, it would seem that a truly capable system would need to be practically infinite, no?