Well this is easy: no finish.
Go back far enough and there's no doubt wood would have been left unfinished and the no-finish option is still widely used today, sometimes by necessity1 and sometimes by choice2.
This may or may not answer the question depending on what you're looking for. If you do need something that was actually applied to wood then oils or greases would surely have been first3.
While waxes and resins exist in nature and can occasionally be harvested in pure or nearly pure form they aren't in an easy-to-apply form, but oils are needless to say. And I think that oils might have been more obvious to early people as a way to treat wood anyway — the "hand finish" mentioned in a Comment above by keshlam could easily have provided the inspiration for deliberately oiling wood, rather than have it happen accidentally/incidentally with handling.
 There's nothing suitable to hand.
 Wood finish would interfere with function or would serve no useful purpose, e.g. on a wooden bearing. And occasionally it will be felt the wood doesn't need a finish to look good, e.g. when using a dense tropical hardwood which can be shined up without anything applied to the surface.
 Initially, and possibly for a very long time indeed (millennia), these wouldn't be of vegetable origin, but animal origin.