I hung out with a native san guy in Namibia who remembers hunting giraffes with bow and arrow with his dad. (he still uses the bow he made)

He said when they killed something that big they would light a signal smoke fire and the entire village would come to the and basically have a party until it was all eaten.

Drying meat out over smoke will help to preserve it, as the CO and other emissions and heat will kill off bacteria and slow the growth of new colonies. It's pretty easy to discover by accident- meat that's been overcooked on a wood fire will last longer than meat than meat that isn't.

Other cultures did things like ferment meats and salt cure them, but if you're inland away from easy access to excess salt, it's pretty hard to do that and not get food poisoning.

As others said, smoking and drying are likely, but they could have also buried food the way many canines do. In colder climates, it can be left outside in winter and the colder parts of fall and spring.

Not necessarily time period appropriate, but Native Americans would preserve meat as pemmican.