It was a plasma of quarks and gluons first (these particles make up protons and neutrons and other unstable particles) which did cool down and become these particles. [https://en.m.wikipedia.org/wiki/Chronology_of_the_universe]

There is no reason to prefer any of the possible particles, but as all of them are unstable - minus the proton - they eventually decay to that state. (neutrons are not unstable in nuclei and such).

NB: this is quite simplistic and I skipped many details