You present a plausible conceptual model of the core principle of a greenhouse gas. There are numerous questions between your conceptual model and explaining what fraction of the observed warming can be attributed to that effect.

What other side effects do the elevated levels of CO2 have on the climate that might also affect the temperature?

What are the second-order effects from the additional heat introduced to the climate by the greenhouse effect? Does it cause more clouds, and if so, what is the effect of those increased clouds on the radiation balance? Changes in precipitation? Vegetation growth?

What other atmospheric constituents have had changes to their levels that might have also changed the climate?

What other non-greenhouse-gas-related inputs effect the global mean temperature? Solar output? Deforestation? Can we accurately model those inputs so that we can sum up all contributing factors and see that it agrees with the observed record?

What other natural sources of CO2 exist and how much is produced by those now and in the past?

And then there are measurement accuracy questions:

Do we have an accurate measurement of the global mean temperature? How far back is that measurement reasonably accurate? What sampling biases exist due to the siting of airports near large urban areas? Of the 5000 odd airport weather stations for which we have reasonably long historical records, more than 2000 are in the United States and large swaths of Africa and Asia have few to none. How does this affect our ability to reliably measure the global mean temperature? We have very limited measurements of the air temperature over the vast area of the world' oceans. How do we deal with the obvious uncertainties that exist due to this?

Speaking of the global mean temperature, what exactly is the definition? You can't actual measure that directly, so you need to carefully define what it is, create a model to allow its computation, and then apply that model to the raw data. Here's an example: Global mean temperature at a given time is the instantaneous integral of the air temperature at 2 meters above the surface of the Earth. But we just have hourly sampled temperatures (that are not even at a consistent time within each hour) at a few thousand locations worldwide, so our model will be to correct the time offsets by linear interpolation with the temporally adjacent samples. To be able to sample the Earth uniformly for the numerical integral, we'll need to interpolate between triangulated stations and correct for elevation changes and proximity to large bodies of water (both of which are extremely complex models themselves). All this doesn't even deal with missing data (extremely common) from the station network. And what do we do over the ocean?

How far back do we have accurate measurements of CO2 concentration in the atmosphere?

Do we have a good measurement of the integrated reflective spectrum across the Earth's surface?

All of the above combined requires a complex physical and numerical model that is very far from your toy example of pure measurement. Such a model is necessarily an approximation with unknown inaccuracies, and the only way I can think to test any proposed model is to wait and see how well it predicts the future.

I'm not asserting that global warming is not happening or that it is not caused by humans. I've just not read or heard anything that answers that question in a convincing manner and I can think of no way to get to a firm answer than producing a model of the global climate that can accurately predict the future and to use that model to measure the fraction of observed warming that has been caused by human-produced greenhouse gasses (and other human-caused climate inputs). And some statistics on a keyword search of climate science papers by social science researchers is not going to convince me or anyone else capable of critical thinking.