When non-specialists use "set" they usually mean "finite set" or "finitely schematized set" or maybe at most "recursively enumerable set."

There's no guarantee the universe is reducible to any of these (although in the likely case the universe is finite in space and time there will be some degenerate case of formulas for everything which "happened" - imo less satisfying than even an approximation via some small set of axiom schemata).