Depends how much time you can invest in aoc I would say.
If you are in your teens and can play 6-8 hours a day, probably it can be done in 1.5-2 years. For me, it took me around a solid 2 years to get to 2k during Gamepark/IGZ. Played at least 8 hours a day on average. Actually maybe more like 10-12 total a lot of days if I add up watching recs and analyzing them.
It depends on how much investment you want to give to it.
I've used to give aoc lessons and the biggest mistake is that new players or even old but non skilled players, want to reach 2k from 1500-1650 level within weeks playing few games on the weekend.
To improve, as anything in life, requires practiser and persistancy .
If a player really commit his time and effort to practise, start learning build orders, strategies, how to play with diferent kind of maps, they will improve for sure. But it takes a long road for it.
I started to play 01/01/2015 playing once a week for some hours .. when I started to play more in 2016 I improved to 1800 HD. Around June I first reached 2k hd (1600 voobly) then in early 2017 I switched to voobly.
This year in may I reached 2k voobly for the first time. So it took me around 2 years when I decided to play more. The first year I was just really noob.
But I’m only 2k+ on arena on other maps my level is different. So to become a full 2k on all maps improve need another year.