Why didn't the Big Bang produce many heavier elements than helium?

By the time helium nuclei could exist in large numbers without being destroyed by the intense radiation field, the universe was about a minute old and the temperature and density were rapidly decreasing. Nuclear fusion reactions to produce heavier elements were possible, but the combination of two helium nuclei or a hydrogen nucleus and helium nucleus produces unstable nuclei. The combination of three helium nuclei produce carbon, but by this time the density of the universe was too low for many three-body collisions to occur. Thus the production of heavier elements had to wait until stellar nucleosynthesis.