If no one mentioned it yet, a problem similar to yours can happen if the freehub isn't a bit sticky. As you coast to a stop, or back pedal a quarter turn the freehub causes slack in the upper loop, which you may feel as a skip when you start out.
Similar, but not quite the same thing, is auto shift one position when you backpedal to get ready to start. Now the chain is wrapped half on one sprocket and half on the other as if you were mid shift. When you start back out that section in transition comes to 12:00 and you feel the skip as the chain takes up that bit of slack.
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