The easiest thing I can think of at beginners level to make those starts smoother would be to use a double handed move (i.e. you take both the ladies hand before you start dancing), typically an armjive (not that I am a fan...) or an in-and-out. They would both allow you to move the follower when you want it, and have some time to get in tune with the beat before you start the dance with the next move.
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