How fast does Narcan (naloxone) typically work?

Depends on how given. If given intravenously, it works literally in seconds (10-20 seconds to start working, works fully in couple minutes); if given intramuscularly (im) it takes 2-10 minutes to kick in. If given in a nasal spray (which is being used in several communitites to help addicts and their friends treat od) it works in-between IV and im, starting in 1-2 minutes, and taking full effect by 5-10 minutes.
Really fast. If Narcan (naloxone) is given IV to overcome an opiate od, the effects are almost immediate. If it is given im the response is slower.
Administered how? “Naloxone has an onset of action within 1- 2 minutes following IV administration & within 2 -5 minutes following subcutaneous or IM administration.” REF: https://www.fda.gov/downloads/advisorycommittees/committeesmeetingmaterials/drugs/anestheticandanalgesicdrugproductsadvisorycommittee/ucm522690.pdf . Intranasal is similar to intramuscular.