Crusader Kings III

Start as a Bedouin culture (I played as Najd) as they have the avid falconer tradition. Your hunt activity should then have a twelve month cooldown, so go on a hunt every time you can afford it, and choose a falconry hunt. I made a custom leader with the hunter lifestyle trait (I don't know if that is optimal, but it seemed appropriate from a role playing perspective), put all of the remaining points into prowess, and made him age 18. You need to earn 100 experience points from falconry hunts to max out the falconer track. In my experience you earn between 3 and 15 experience points from each falconry hunt. You get more points if you succeed in the hunt, and more points from choosing options that increase experience gain. If there is a game sighting relevant to falconry, make sure you hunt in that province. Run the game at speed 5, pretty much ignore most other things, and go on a hunt every time you can.