Objection: Correlation is not proof of causation. There is no proof that CO2 is the cause of current warming.
Answer: There is no “proof” in science — that is a property of mathematics. In science, what matters is the balance of evidence, and theories that can explain that evidence. Where possible, scientists make predictions and design experiments to confirm, modify, or contradict their theories, and must modify these theories as new information comes in.
In the case of anthropogenic global warming, there is a theory (first conceived over 100 years ago) based on well-established laws of physics. It is consistent with mountains of observation and data, both contemporary and historical. It is supported by sophisticated, refined global climate models that can successfully reproduce the climate’s behavior over the last century.
Given the lack of any extra planet Earths and a few really large time machines, it is simply impossible to do any better than this.
Aside: It is usually interesting to ask just what observations or evidence your skeptic would consider “proof” that global warming is caused by rising CO2 levels. Don’t be surprised if you get no answer!