Yeah, well, there is the nub of the argument, and a good part of the reason why most scientists accept that humans are affecting climate but many disagree about the importance of the human role. It is also where a lot of uncertainty appears in predicting into the future.

The problem is that there is no "signature" we can measure directly and say "this 23 % is from humans (pick any number), and the other 77% is what nature does".

What we have are climate models. The climate models are an attempt to imitate the natural system behavior, and seeing how different changes to input conditions cause changes to output. The system is complicated, and so are the models.

There has been a lot of work on trying to figure out how much change has been "forced" by human activities versus how much can be explained by natural changes. They can compare models with, or without, changes to various important parameters over time as an input, and see how the results differ, and then interpret what is really important and what is not so important for what is actually happening. Fairly complicated work in actual practice.

It is from playing around with the various parameters that can affect climate, and finding mismatch between observation and the changes that ought to have happened if nature alone is the cause, that a lot of climate scientists have concluded that CO2 is the main problem.

Are they right? We are finding out. Not sure it is wise to perform this experiment in real time, but we are, even if not purposefully.