As an adult I learnt to speak Japanese. Japanese has a pitch accent that is used to discriminate certain words. For example 箸 (chopsticks) and 橋(bridge) are both "hashi" but with a different pitch accent. Event though I spoke Japanese for years I couldn't hear the difference. With isolated words spoken slowly and carefully I could maybe perceive some difference, but in normal speech at normal speed it just wasn't there. Even without this I could have normal conversations without issue so it didn't bother me too much.
One weekend I sat down and spent the entire weekend listening to words and guessing the pitch accent. Hear word, guess pitch accent, check answer. I must have spent a good 10+ hours doing that. Thousands and thousands of words. After a while I could actually hear the difference. For me it didn't feel like a difference in pitch, more like a subtle difference in emphasis. It's a very hard feeling to describe. It kind of feels like learning to see a new color. It was always there but you never noticed it before.
Another goal of mine is to learn relative pitch for music. There are training apps out there and I'm convinced that if I do a similar amount of practice on mass I will be able to hear the difference between a fourth and a fifth and so on.