Hydrogen was not "created at the moment of the big bang".
Particles (leptons and quarks) can attain mass via the Higgs field after the epoch of electroweak symmetry breaking, that occurred about a picosecond $(10^{-12}$s) after the big bang. Only after this was it possible to form the building blocks of hydrogen.
In fact the formation of stable protons comes "much" later at about a millionth of a second. Most of the mass of a proton does not come about from the HighsHiggs field, but from the binding energy if it'sof its constituent quarks.
Hydrogen (the atom, rather than the proton nucleus) forms much, much later; about 400,000 years after the big bang.