You're right that there is no mechanism to make primordial black holes in the standard theory. That's because they're new, separate things, so to have them, you of course need to add in new ingredients.

They can be created by the collision of topological defects in the early universe, which in turn can be created in phase transitions during the cooling of the universe, like imperfections in quickly frozen ice. Or they can be created by simple collapse following inflation, if inflation is modified to create large inhomogeneities.

You don’t need to matter to create a black hole, a Kugelblitz black hole is made entirely of light.