There can never be "proof" of human-induced climate change – and we shouldn’t look to science to provide that. Science is about the estimation of likelihood based on available evidence. There will always be uncertainties because the earth-atmosphere system is too complicated to be understood in intimate detail. So judgement is required.
There are two possibilities: either climate change is human-induced or it isn’t. Despite some inconsistencies in the former possibility, the available evidence is overwhelmingly at odds with the latter. If faith can be described as belief held despite a dearth of supporting evidence, then the "sceptical" camp has a far greater need to cling to it.