What about having a weight that the solenoid holds up and allows to drop, kicking the ball, not sure how heavy it'd have to be or anything, just throwing possible ideas out there (and you may have requirements that don't allow that)
What about using mechanical advantage to increase the speed of the blow delivered to the ball. If the solenoid were attached to the shorter side of a pivoting arm (a lever), then the longer free end of that arm were used to impact the ball, you might get better kicking distance because of the increased speed.
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