To sync your Xbox 360 controller without the sync button, you will need to use a USB cable. Here are the steps to follow:
1. Make sure your Xbox 360 controller is powered off.
2. Connect the USB cable to the port on the back of your Xbox 360 console.
3. Plug the other end of the USB cable into the Xbox 360 controller.
4. Turn on your Xbox 360 controller.
5. The Xbox 360 console should detect the controller and you will be able to use it without needing to sync it.
If this does not work, you may need to reset the controller by removing the battery pack and disconnecting the controller from the console. Then, repeat the steps above. If you are still having trouble, you may need to try a different USB cable or reset your Xbox 360 console.