Cheaters are by definition anomalies, they operate with information regular players do not have. And when they use aimbots they have skills other players don't have.
If you log every single action a player takes server-side and apply machine learning methods it should be possible to identify these anomalies. Anomaly detection is a subfield of machine learning.
It will ultimately prove to be the solution, because only the most clever of cheaters will be able to blend in while still looking like great players. And only the most competently made aimbots will be able to appear like great player skills. In either of those cases the cheating isn't a problem because the victims themselves will never be sure.
There is also another method that the server can employ: Players can be actively probed with game world entities designed for them to react to only if they have cheats. Every such event would add probability weight onto the cheaters. Ultimately, the game world isn't delivered to the client in full so if done well the cheats will not be able to filter. For example: as a potential cheater enters entity broadcast range of a fake entity camping in an invisible corner that only appears to them, their reaction to it is evaluated (mouse movements, strategy shift, etc). Then when it disappears another evaluation can take place (cheats would likely offer mitigations for this part). Over time, cheaters will stand out from the noise, most will likely out themselves very quickly.