Causation between human activity and climate change resulting in that temperature anomaly, is fundamentally hard. Especially in a field like climate science where every model carries a big bundle of assumptions some of which are just educated guesses.
But the models for anthropogenic climate change have been pretty bang on at predicting the temperature anomaly that we're seeing today. That doesn't formally prove causation but it's certainly enough evidence that we need to start acting to mitigate climate change now, there's no more 'complicated analysis' needed. At this point it's a bit like arguing over whether hitting the iceberg is really what's making the titanic sink, while standing on the submerging deck.