I'm not sure how long exactly. I played with the wiki open for a fair bit. The help in nethack is pretty descriptive for keys. You end up remembering the ones you use the most pretty quickly. Some of the more obscure ones I forget.

Something about the complexity of the controls is part of the charm for me though. Suddenly you remember you can do something you totally forgot about and it changes the way you play the game. Or you reach some kind of understanding about one of the mechanics that just makes it part of your play style.

I've played a lot of different roguelikes, nethack and its variants are some of the few I still get that feeling of discovery from, despite playing it for years, scouring spoilers and even looking at parts of the source for fun.

It's easier than learning vim, that's for sure. Try following the guide from the wiki at first. [0] After a while you'll be navigating the UI subconsciously. Don't be fooled by this though, the game itself is quite unforgiving if you don't know the mechanics and aren't thinking ahead.

[0] https://nethackwiki.com/wiki/Standard_strategy