Most people can sensitize themselves to the difference between similar sounds at least somewhat, but you might not develop as fine a perception of it as you would have if you’d grown up with a language where nasality mattered more. One way to do it is to listen to minimal pairs and guess which is which, which is slow going, but most people will eventually make headway. It’s significantly faster if you have a native speaker who can say them instead of playing a recording, and even faster if they let you touch their face while they do, but that’s awkward for most people.
Just to probe a little, /n/ and /ŋ/ are both nasal, they just differ in place of articulation- is it maybe just a difficulty perceiving nasal sounds generally as opposed to distinguishing them from non-nasals? I would generally give the same advice either way, but you might want to critically listen to people from where you grew up, maybe they don’t enunciate much between the two sounds.
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