If regulated work has already started, continuing without clarifying the permit requirement can make the problem larger. Document the current condition and contact the issuing jurisdiction before covering or advancing work that may need inspection.
Building departments use their own terminology, deadlines and procedures. Treat this as a practical orientation and verify the current rule with the jurisdiction that issued — or would issue — the permit.
A city may allow an application after work has begun, but additional requirements or enforcement consequences can apply. Ask the responsible jurisdiction.
Do not assume you can continue regulated work. Follow the city's direction for the specific project.