Interesting question - first sub 20 single was after about 2 months, first Ao5 after about 4 months, first ao12 about 6 months, first ao50 about 9 months. Would've been much quicker, but I only cube for about 45 mins a day, and not at all on weekends.
It's my 1st cubiversary today, and my last 6 ao50s have all been sub 20. So it depends how you classify 'being' sub xx. Personally, I'd only just now consider myself sub 20, as my global average is about 19.5. I regularly get 17 or 18 second ao12s, but I'm a long way from being sub 18.
There's been posts in the past about how to calculate when you're sub xx mathematically, but I think it's far easier than that - I used to be ecstatic when I got a sub 20 single, now even 20.00 is a disappointment. IMHO when you start being annoyed by single solves that are sup xx, it's a pretty good indicator that you're sub xx.