Interactions with the Higgs field only generate about 1 percent of ordinary mass. The other 99 percent comes from phenomena associated with the strong force, the fundamental force that binds quarks into protons and neutrons that comprise the nucleus of the atoms of ordinary matter.
Because there wasn’t an equal amount of matter and anti-matter in the early universe? That solves the problem. Case closed? Of course not. Because physicists make a living from solving problems - so they have an incentive to create problems.
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