The sheer amount of evidence that the effect is indeed predominantly human-caused is so vast and convincing that at this point, failure to accept it reads like closed minds repeating the "No true Scotsman" fallacy.
It's been below 300 ppm for at least the last 800,000 years, had now increased to over 400 ppm in a pattern that directly maps to the industrial revolution, radiocarbon dating traces the carbon in the atmosphere to "old" carbon like that from fossil fuels, and the known sources of human emissions adequately explain the increase.
An argument based on likelihoods and probabilities is not anywhere close to rock solid proof, since the credibility of the folks determining those is what’s doubted in the first place.
Even if aliens with no human context at all showed up, a full proof will still convince them via pure logic and deduction from basic axioms.