Consequently, the only new elements cooked up by the Big Bang were helium, which has two protons, and lithium, which has three. Astronomers and physicists are very confident in their assertions about what went on 15bn years ago in the Big Bang. One reason is that the physics involved is well developed. A more interesting reason for confidence is that models of the Big Bang predict that hydrogen and helium should exist in the same proportions everywhere in the universe. The prediction holds up well.
Astronomers can tell the mixture of elements in a star from the colour of the light it emits.
Fortunately for us the primordial mix of elements produced by the Big Bang gets cooked further in the stars. The type of cookery depends on the size of the star. The heating is produced by gravity squeezing the material together, so bigger stars get hotter and burn faster. Our sun, which is 15m C inside, can only make helium. The crucial reaction for generating heavier elements is the fusion of three helium nuclei to make carbon.