If you have systems which can propagate copies of themselves imperfectly and that have a varying environment to contend with that has effects on their ability to propagate, then the subsequent copies of those systems will undergo an evolution of forms with a selection bias.
Mathematically you can demonstrate this pretty conclusively.
Then all you really need to do is demonstrate that there are systems in the physical world that meet the set of criteria required for evolution to occur and you can then be pretty sure that evolution is occurring.