MaxQ

At what point is presentation of physical laws (thermodynamics), experimental demonstration of phenomena (energy in certain wavelengths being trapped by specified molecules such as CO2, H2O, etc) and measurements of change in heat energy capture of the planet while also calculating how much these atmospheric molecules have increased directly due to human activity, considered to be approaching proof?

1.If more energy is poured into a body than is allowed to escape, then the temperature of the body must rise to achieve equilibrium.
2. Certain gas molecules block energy release. CO2 and Methane are examples
3. Man's activity has raised the number of these molecules above what would be from otherwise normal processes.
4. The amounts in the atmosphere can be, and are, measured. The increase in energy capture can be calculated as well.
5. Paleo data is available for times of similar gas concentrations and associated temperatures.
6. This is key: Specific feed back areas will make for variances; there will be errors in data collection and short term interpretations and conclusions; the planet is an emergent property that will sometimes react in a manner not completely anticipated (particularly in regards to time)....HOWEVER....the overall trajectory of the physical processes are well understood with the general outcomes as near a certainty as we mortals can speak of. In other words, the details may vary, but the trajectory of overall global warming will pretty much match the amount of greenhouse gases that result from Mans activities.

I personally have zero expectation of mankind taking any steps significant enough to reduce the annual addition of greenhouse gases. The temp of both the atmosphere and oceans will increase accordingly. The acidity of the oceans will continue to increase. All processes affected by these increases will accelerate. Sever weather, droughts, fires, sea level rise, etc which in turn affect our civilization. Famine, migrations, wars, economy stresses/collapse...which all have additional feedbacks that will probably cascade.

At some point the increases from Man's activity will slow significantly as a result of all this fun stuff. If we lack the wisdom to limit the output of our technological success, Nature will limit them for us. She has a long and honored tradition of doing so when any of her populations indulge in overshoot.
These kids referenced by the original poster are protesting against this dystopian future. I expect their efforts to be fruitless, but at least they are trying.
Man is quite clever, but He is not wise. He tends to believe what he wants to believe. Proofs seldom can penetrate that emotional armor.