Why is the era of nucleosynthesis so important in determining the chemical composition of the universe?
Big Bang nucleosynthesis happened long after the Big Bang by which time matter was already dominant.
Soon after the Big Bang elementary particles were formed. For some reason, which is now thought to be due to a predominance of neutrinos over antineutrinos, mater became dominant over antimatter. Had the amounts been equal the Universe would just contain photons.
Some 300,000 years after the Big Bang, the Universe was cool enough for atoms of Hydrogen to form. Big bang nucleosynthesis fused Hydrogen into Helium and small quantities of Lithium and Beryllium.
The heavier elements were all formed inside stars and as a result of supernova explosions.
So the early period of the Universe preference for matter over antimatter was the most important factor in determining the chemical composition of the Universe.