Think OP's argument is probably a very strong argument but need to see his math and some sauce on manufacturing rates and number of actual manufacturers to better understand his argument.

The manufacturing of the vaccines is sometimes done in-house by the vaccine developer and sometimes it's out sourced. So how many manufacturers are there? What are their production rates? How many bottling lines are they using? Does one plant have ten bottling lines? Is the rate out of one plant one per second or ten per second?

What's the world cumulative rate?

If they're clearly faking it then this argument is devastating. Someone needs to do the research.