You really don’t understand this stuff, do you Lees?
If I want to prove AGW statistically I need to formulate the alternative and null hypotheses. As one who knows AGW is happening, like you and me, the alternative hypothesis has to be: temperatures are increasing. That is what we are testing, after all.
The null hypothesis has to be: temperatures are steady.
This is just the logic needed, there is no “official” alternative and null hypotheses.
The null hypotheses can be tested—we do have the weather records going well back.
If you don’t understand this then buy the Stats for Dummies book and have a read.
So we formulate our alternative and null hypotheses. We look at the data and we find, of course that temperatures have not remained constant, they have increased significantly. So we reject the null hypothesis and accept the alternative hypothesis.
We can also look at GHGs in the atmosphere: they are increasing. We know from spectrometry that the GHGs absorb, overall, infrared radiation coming from the surface and again we show that global temperatures are increasing.
Global temperature increase animation:

Makes it pretty clear that global temperatures are increasing and are increasing more and more rapidly.