There's plenty of science that works like this, generally in fields where the systems under study are very large and complex.
The example I often see used is the link between cigarette smoking and lung cancer. This seems like an obvious thing, but it's actually extremely hard to really prove (or equally, disprove). You have an event (smoking a cigarette) and the consequence (lung cancer), but in between you have perhaps 40 years of other health events. How can you possibly prove a causal relationship?
The answer is that in an individual case, you can't prove it. But if you take many people and painstakingly track them over a long enough period you can slowly narrow confidence intervals until, at some very ill-defined point, the case tips over and changes in the minds of people in the field from interesting unproven hypothesis to proven fact. You can also test parts of the theory in the lab (chemicals in smoke causing DNA damage, for example) and generate further hypotheses to test in people. It all adds to the evidence.
AGW is similar in that we'll probably never have 100% proof, it's not even obvious what that might look like, but we can construct a quite detailed model of the system and gather supporting evidence. Again, at some point, if no alternative explanation is found, it tips over into case proven.
I'd also distinguish between science, which tries to understand what is happening to the climate, and policy recommendations.
Your objection seems to be to policy recommendations, and I can understand that. I think policy is the domain of politics and there should certainly be a great deal of political argument about what we should do, or even if it's worth doing anything. However your post seems to be arguing policy by attacking science, and that feels wrong to me.