What about, for instance, all the successful engineering that is driven by models of complex systems? We don't understand bridge dynamics at an atomic level, we have complex models that require a lot of specialized education to create, understand, and use. Same goes for microprocessor engineering. No human understands the design of a modern CPU at a transistor level, that design is also handled by computers (again guided by humans with specialized education).
We can build bridges and build microprocessors. No one has bottled up one "Earth's atmosphere" in a lab and run controlled experiments on it. It's not empirical.
We have decades of data at this point that it has been getting warmer, and that less energy has been escaping into space specifically in the spectrums that co2 traps ( from satellites), in exactly the amounts expected from the c02 delta we have measured over that time (from isotope analysis, we can tell that WE added it via burning fossil fuels)
It is as certain and clear as science ever is. The idea that it isn't is due to propaganda that is very convincing.
It is extremely far from as certain as science ever is. Randomized, controlled experiments are as certain as science ever is. This is pretty far from that.
The evidence is as good as any non-controlled experiment is going to be, perhaps. But it's pretty important that we not confuse these kinds of descriptive results with the actual certainty that comes from high powered controlled trials.
It's extremely easy to make reasoning errors in descriptive data analysis, that look very convincing.
People actually did do just that. Historically, high altitude balloons where used study the atmosphere and gather temperature, pressure, etc. Then it’s just a question of shining light through various atmospheric mixes to see how they respond to sunlight. Rockets and satellites then refined our understanding over time.
The basic question of global warming is a fairly simple physics problem, it’s because people care so much about absolutely tiny differences that such complex models are used. Aka Mercury vs Venus surface temperatures closely line up with simple models, but on earth people care about +/- 0.1 C and even more so in terms of local weather patterns.
The point is that the models and their accompanying scientific descriptions provide explanatory power that is a valid source of knowledge even though it is not empirical (empiricism is a false epistemology, but that's a topic for another time). If you have a bridge design produced according to good models, and another bridge design produced without using any such models or engineering knowledge, the epistemological status of the claims "this bridge design is safe" is different between the two bridge designs. That is true even before each bridge is actually built, and if it weren't true, then there would be no reason to have laws requiring bridges to be built according to certain standards (since "we wouldn't know if it's safe until we build it").