Why didn‘t the big bang create mostly iron as it cooled and expanded? Iron is more stable (considerably) than hydrogen.
The big bang created only the lightest elements, hydrogen and helium, some lithium, and very small amounts of beryllium and boron isotopes. Beryllium isotopes have a total of 10 to 16 protons and neutrons in the nucleus only Be10 is stable. The universe wasn't hot enough at high enough pressure long enough to fuse carbon or anything heavier on the periodic table together. It takes massive stars millions of years at very high pressures to create iron. Even stars can't fuse iron into anything heavier because it takes too much energy to create the heavier elements that are created only in super novae or linear accelerators.
If you are asking why nuclear reactions did not proceed to iron in the early universe, the way that they do in stars, then the answer is that the early universe, when it was hot enough to fuse, was much less dense than the core of a star. Because there are no even remotely stable isotopes with mass number 5 or 8, the collision of a single proton with a single helium-4 or two helium-4's will not do anything useful. To proceed to heavier elements than helium, typically you need a simultaneous collision of 3 helium-4 nuclei in what is known as the triple-alpha reaction. Since this reaction requires two simultaneous collisions, it requires very high densities to run, not just high temperatures. So the fusion process in the early universe, not having very high densities, could not generally proceed beyond helium.
Iron is a lot more complicated - hydrogen, with just one electron and one proton, is as simple as it gets. Also, it takes a lot of pressure and heat to create iron - hydrogen is easier.
