Ya know, I saw this a year ago, and was curious if it actually held up. After all, the amount of CO2 released by humans is only about 4% of all CO2 released, on an annual basis (730 gigatons all sources, ~30 gigatons by humans).
But it's a pretty simple equation. We know the approximate mass of the atmosphere, and the number of molecules per weight. We know how many molecules are in a unit mass of CO2.
Thus we should be able to calculate out "how many gigatons of CO2 are necessary to increase atmospheric CO2 by 1ppm", and then given measurements of actual CO2 increases, how much CO2 is necessary to increase atmospheric levels by the amounts seen.
If the amount of CO2 required to yield the observed increase is greater than annual human emissions, then that's a strong signal that CO2 increase is NOT anthropogenic and something else is going on. If it's less, then that is a strong signal that humans are the primary culprit.
Anyway, I did out all the math and it takes about 8.8 gigatons to increase atmospheric levels by 1ppm, and we're netting an increase of about 17gt into the atmosphere per year, for an increase of ~2ppm annually. So it's pretty clear that this is anthropogenic.
If anyone wants to check my math I wrote it all up here [0]. Numbers are a couple years old at this point but the conclusion still stands.
[0] https://biotinker.dev/posts/climate1.html