When can I change to synthetic oil?
The simple answer is - after your machine is done breaking in. This opens a whole additional can of worms, but the reader should draw his or her own conclusions about break-in.
Essentially, the reason that it is harmful to put synthetic in too early is because it is too effective at protecting your engine from wear. During break-in, especially in the first couple hundred miles, your engine will be filing itself smooth, most notably the piston rings and the cylinder wall. As this occurs, the clearance between the rings and cylinder walls gets closer and more consistent. Imagine a piece of sandpaper. There are peaks (the grit) and valleys (the spaces between). If you set this on a piece of wood, you will still have gaps in the valleys, even though the peaks are touching the wood. But, if you rub the paper on the wood, the material it removes will allow the paper to sink in closer to the wood, slowly removing the gaps until there are essentially none. This is a simplified description of break in.
In order for this to happen in your engine, between two metal parts, you need metal on metal contact. This occurs when the sharp, small points left over from the honing of the cylinder wall actually break through the layer (or film) of protecting oil and get trimmed off by the piston rings going up and down in a consistent path. This creates the shimmering layer of metal flake that is in the oil the first few times you drain it. Ever wonder why it's called "break-in"? Well, now you know... because things are breaking.
When you add an oil with superior film strength (more difficult to squish all the oil away from between two moving parts) to an engine that has not been broken in completely yet, the small points on the cylinder wall are unable to completely break through the film to make contact with the piston rings, and subsequently are not filed off. However, since the pistons are now riding on a smaller surface area (just the points, instead of a smoother, worn surface) heat will build up in those places quicker, and the piston will have more difficulty bleeding off heat to the cylinder walls (pistons don't have any active part in the cooling system on most engines). This buildup of heat will wind up glazing the cylinder walls and piston rings, which in turn will make it very unlikely for the peaks to ever get worn off by the rings. This means that your engine will never fully break in and will be down on power compared to a properly broken in engine. It will consume more oil as well.
A good time to go to synthetic in your Ninja is at the second oil change, 3500 miles. (Kawasaki recommends 6000 miles for the second service, but, especially during break in, it's best to change it more often.) You may end up changing your oil several times before then, but it's best if you wait until 3500, or even 5000, miles before you put in synthetic. You don't want to do it too early and risk not getting a complete break-in. And remember, changing your oil regularly is the most important thing about oil.