Give every offline channel a unique detectable fingerprint: a dedicated phone number (billboard), a memorable URL or QR code with UTMs (radio: 'yoursite.com/radio'), a named offer ('mention the morning show'), and the intake question. 'how did you hear about us?'. Logged religiously.
Then triangulate with timing: branded searches, direct traffic, and calls in the weeks a campaign runs versus the weeks before. Offline attribution is never precise; a clear lift pattern plus fingerprint counts is honest evidence.
Decision standard: cost per attributed customer within 2x of your digital channels keeps an offline channel alive (its unmeasurable halo covers the gap). Nothing detectable after a fair run. The fingerprints answered your question.