I’d like to provide an answer (even if it’s an old question).
I always thought you could enter "Download Mode" by simply holding the Volume Down and Power button when turning on the phone. However, Samsung changed the process to the following:
- Connect a USB cable to a powered-on PC or Mac (it won’t work if it’s not connected to a data source). Dont put it into your phone. Not now.
- Turn off your phone.
- Press BOTH Volume Buttons (+ / -) simultaneously. (No, don´t press the Power button or any other buttons than V+ and V-)
- Plug the USB cable (connected to the running PC/Mac) into the powered-off phone. Again, do not press the Power button!
- The phone will automatically turn on and enter "Download Mode," where you’ll see the wanted options.
(Note: Maybe you must first unlock the hidden “Developer Menu” and enable “USB Debugging.” You might also need to enable “OEM Unlock,” which only becomes visible after using the phone with an active internet connection.")