Can someone explain how elements are generally modeled to have formed from the big bang? And is there anything that it Jacob may be missing in the current literature?
Yep. Jacob's quite right about nucleosynthesis in the Big Bang, but that's not even close to the only nucleosynthesis pathway out there.
First-generation stars (called "Population III", confusingly) are thought to have contained almost no elements heavier than helium, which may have allowed them to stably reach much higher masses than the current generation can manage. Mid-weight elements up to the mass of iron are formed through one of the several fantastically complicated fusion processes which occur as older stars deplete their fusible hydrogen and start accumulating helium in their cores; carbon in particular is generated mainly through the triple-alpha process. Elements heavier than iron don't release energy when fused, so stars can't produce them in quantity; they're instead produced mainly by fusion events during the early stages of a supernova.
I thought this may be of interest to the LW community. Jacob Barnett is a 12-year old male who taught himself all of high school math (algebra through calculus), has a currently scored math IQ of 170 (for what that's worth) and is currently on track to become a researcher of astrophysics. His current major news worthy claim-to-fame (aside from being really young): The Big Bang Theory is currently incorrect (I believe the article states he has something about a lack of carbon in the model), and he's planning to develop a new theory.
I haven't learned anything serious in physics, so I have nothing to note on his claim. I realize the news article cited puts him claim fairly generally, so I'll ask this: Can someone explain how elements are generally modeled to have formed from the big bang? And is there anything that it Jacob may be missing in the current literature?