My car would not start. I rocked it back and forth and it started. New Ssarter

Cold it have been the starter made contact with the ring gear/flex plate teeth and jammed and caused the starter to stick or by rocking the car back and forth that you dislodged the starter contacts and plunger? Any reputable repair shop wold charge $60 max to check it ot.

Sounds like a nuetral safety switch.