What transfers substances to the brain faster than when a drug is injected or swallowed.

The answer is smoking.

Intravenously is usually faster msthod route of intake. Depending on the question though, this may count as injection... In which case mucose membrane via the facial mucosa like the olfactory nerves and mucosa, or the sublingual or oral mucose. The olfactory route is usually the fastest as some substances can travel the short distance via the nerve or the through the vasculature or the membrane. Cocaine is the biggest example.

Conjunctival membrane;