I'm not studying Mandarin anymore right now because I'm focusing on German and Japanese, I quit when I was still a total beginner but I could differentiate the tones perfectly, and it happened immediately. Cantonese is a bit harder.

I don't have what they call absolute (or perfect) pitch, but for example if I hear a melody I've never heard before I can play it by ear immediately with only a couple of mistakes, so maybe it's a matter of musical ear versus being tone deaf?

It's not like you learn to hear pitch, it's like asking someone how long did it take you when listening to music to figure out if a note is higher or lower than another? How long did it take you to tell different colors apart? It's how the ear and eyes work by design. Rather, you can learn to pay attention to things your ears already perceive, but you never paid attention to those details before.