What does belief have to do with this? This is a scientific question, not a matter of belief. Proof is what is and should be persuasive. There are indicators that AGW is occurring, they are just not at the level of proof. I went into detail on the models to show why they are particularly misleading and often used to convince people that we have more scientific certainty than is possible.
Ah, I see, you want scientific proof. Absolute proof that practically eliminates all other possibilities. Proof that is so certain, so precise that we can predict with a great deal of certainty exactly what the outcome will be for any given change.
I believe your thinking of mathematics, not science.

Science is more about different levels of certainty. You never have absolute certainty, absolute proof. You have more or less certainty. Some explanation reach a high level that they are labeled theories, but even the most hallowed theory is not considered immutable if new facts dispute it.
So asking for "proof" is unachievable. Science doesn't "prove" anything.
But what we can do is ascertain and compare the levels of certainty.
For instance, we are very certain that higher concentrations of CO2 in the atmosphere trap more heat. So certain that practically everyone agrees with that theory.
That the Earth's atmosphere has been warming over the past century and half is also fairly certain, when you consider not only temperature readings but climate-related changes in plant species locations, animal (especially insect) ranges, glacial melting, etc. There are far more indications of warming than of not.
And we have reliable measurements of the CO2 concentrations in the atmosphere. So that is very certain, too.
But you dispute how certain we are that CO2 is the main cause of increased temperatures. And here is where comparing levels of certainty is useful.
We are certain that CO2 is trapping heat, which, unless the heat is dissipated, will increase temperatures. So we are pretty much certain that some increase in the temperature is from the higher CO2 concentrations.
We very, very uncertain that increased solar insolance is causing temperature increases. This is because there has not been a consistent increase in solar insolance for the past few decades--the measured insolance has gone up and down, without a marked trend in either direction--while temperatures have been tracking up.
So in comparing certainties, we would say that our certainty of CO2 being a cause of temperature increase is much greater than from solar variances. In fact, we would say that we are more certain that the temperature trend is NOT caused by solar variance and that it is.
This can be applied to almost every objection by denialists to AGW.
This is why I say that denialists need to "prove" their contention that AGW is NOT happening. Because when we look at the various levels of certainty, we are far more certain that CO2 is part of the warming than it is not. We are far more certain that CO2 is probably the major cause of the warming than we are not. We are far more certain that increased concentrations of CO2 will increase temperature than we are not. Relatively, we are more certain of AGW than we are of the objections.
Have we reached a level of absolute certainty about AGW? No, I'll agree with you there. But the
preponderance of evidence is pointing toward AGW. So it must be taken seriously.