The minimal pair training seems to be the best way for adults to distinguish the sound difference on a foreign language that doesn't exist in his/her native language. According to Fluent:
But it’s not all bad news. Linguists have been studying this phenomenon for years and they’ve found a way to help learners hear and pronounce the difference between these tricky sounds.
This method, known as minimal pair training, involves listening to a word that has the sound difference you want to learn (like ship or sheep), deciding which one you think it is, and getting immediate feedback about whether you were right or wrong. After a few sessions, you’ll hear the difference more easily and be able to pronounce them better.
I installed Anki deck (French and English) and tried using it for several days. However, I could not understand many of the sound differences, even in English which I have learned for more than 10 years. For example it's the difference between letter and latter or men and man, as both vowels don't exist in my native language. I failed so many times and while I also tried pronouncing them using the IPA but didn't understand the difference at all, since what I thought I heard and pronounced as A was actually B, and vice versa.
Eventually, I got right not because I was able to detect the difference but because I memorized the sound pattern. It is like this female voice that is a bit high-pitched should be the former word!.
Then, after I tried to hear the word in other voices by searching them on the Internet, I found I could not understand the difference at all. That is understandable as I wasn't able to understand the sound, just memorize the sound pattern to game the system.
I'm actually not even sure why the minimal pairs work. But if you don't understand the difference to begin with, is there still anything you can do, to make your ears detect the sound differences?