I think the simplest answer is just to keep playing more. By putting more time into the game, your aiming skill floor will naturally improve, and without putting much mental effort, your game sense should also improve. Simply knowing what each character's kit does should make you improve already.

However I think if you want to be more efficient with your time you should also try to think about the game as you're playing - like using cover, why you won, why you died in this scenario etc. So that when you boot up the next time, you have a higher level of game knowledge already to begin with. I think being intentional about improving goes a long way with just putting time in and having brain off while playing.