Depends on your work ethic really. You will become what you perceive to be 'good'. It may however take years, or you may become 'good' in a couple of months. The factors that are involved include the amount of hours that you can play the game, mindset (this is actually a big one) commitment to improve and motivation.
The main thing however is that you have fun, in my opinion the game becomes less fun the higher up on the ladder you are as play becomes transparent almost to the point of being predictable. You will enjoy the game a lot more at the lower leagues because you can be diverse in your strategy and creative without the punishment of losing every game where you try something wacky.
But if you're looking for a clear cut answer I would say that considering you have no/little experience in the genre, platinum league can be achievable within a year. If you have experience or are very dedicated you can get diamond within a league. Masters will take a little longer so don't be disappointed if you do not achieve it as fast as you got promoted to the other leagues.
I had little experience in RTS before SC2 and managed to get into gold league after about 3-4 months. Diamond then came after the next 5 and then I achieved masters league another 4-5 months later. Since then I've been stuck in masters until now which has probably been about two years now? So good luck
Hard question to answer and I won't repeat alot of what the other guys are saying, but I hope I can help with my experience.
I started playing when the game was released, I had a little bit of RTS experience with Warcraft 2 (yes, I'm an old gamer 34 years old). Back then I got to Diamond very quickly, 2 months after the game was released and was beating higher level Diamonds. Then I took a very long break due to work, college etc. I recently just made a comeback a couple of months ago and the community is a lot better than they used too be. I placed into bronze because my mechanics had declined a lot and I didn't know any recent build orders. I started playing 10 games per day as well as watching replays and taking note of my mistakes. I got coached by a GM for an hour and that REALLY helped and I think if you want to jump start your skill, get some coaching, it will save a lot of time. I am much better than I was back when I was diamond now but I'm only in the Platinum league. I am beating Diamond players occasionally, which is promising and I think if I keep practicing and studying the game I will be Diamond next season, Master's will probably be a long way off but we will see.
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