Choking
It’s definitely preferable for the patient to be unconscious, so in some ancient cultures, like Egypt and Assyria, patients were simply choked until they passed out, then operated on as fast as possible before they came to. A good knock upside the head would do it, too, though it tended to result in unpleasant things like brain damage. Both options had their risks, honestly, not the least of which was “speed surgery.”
Cocaine
Around 1350, Inca shamans figured out that chewing coca leaves and then spitting into patients’ wounds resulted in a topical anesthetic effect. It might have worked, but it couldn’t have been sanitary, and side effects included incessant rambling and an enthusiasm for synthesizers.