In the original paper on Big Bang Nucleosynthesis by Alpher, Bethe, and Gamow all the elements were formed in the Big Bang. As Stellar Nucleosynthesis became popular it grabbed the creation of heavier elements. Lithium hung around for awhile, but eventually BBN took it because SN didn't want it. There is no distinct reason for larger atoms to not be primordial other than our model is tweaked to fit with other models. Our model predicts population III stars, ones made out of hydrogen and helium devoid of heavy elements, but we don't see any so our model is wrong.