When you set up a new campaign, you generally get an OK QS, how long does it take to get a GREAT QS for your keyword? is it possible to have a GREAT QS straight from the beginning?
It's certainly possible to have a Great QS from the start - most of my keywords do when I set up a new account. If you start out with an OK QS, then Google will gradually change it based on your clickthrough rate, so I would assume that it'll depend on how many impressions each keyword gets, and what the clickthrough rate is.
CustardMite is right. If you set-up your campaign using good combination of keywords+ads+landing page then you can easily have "Great" status on most of your keywords. But if you have "OK" or "Poor", then I think in about a week or two, if you keep improving your CTR, Google will change the status to "Great"
It's very easy to start off with all of your keywords having a Great quality score. You just have to know how to set up a decent campaign. If your keywords are anything less than Great, you're doing something wrong. Just make sure to have a lot of unique, high-quality content on your landing page, which is highly relevant to your keywords and ads. The more keywords you have, the more difficult maintaining relevancy becomes, which is why you need multiple landing pages. By far the most important factor which influences quality score, in my personal experience, is the amount of relevant content: the more there is, the better.