As @Groin said, the modern komi system as we know it, only started to formalize in the mid-20th century, although its early format involved a transition from the teai system (playing many games without komi with different ratios as black or white and handicaps). From my research previously (still not completely), they didn’t just appear out of nowhere, but measures of half a stone or different advantages for the extra “first move” (sente) were used for players of different strengths. And game records with this early “komi” format can be traced back at least to the 19th century (perhaps even older).
And players had known about the “first move” advantage (先手利) for a long time, even going as far back as the first surviving scrolls around the 5th century. I’ve written about it years ago, and there appeared to be some form of “meta-counting” system back then that not only counted “stones” within a game, but across several games (and using different counting units, that is, the first player was given 3 “chips”, and the second player has to win games or use the captured stones to take those chips back in order to “win” across multiple matches, which most likely linked to ancient gambling customs). Although this custom seemed to be lost around the 10th century and mostly forgotten, or was originally only a regional practice. But it certainly showed players knew about the “first move advantage” and the need to compensate one way or another for thousands of years.