Get ahead of someone to obtain something, as in There was only enough for one, so Jane ran as fast as she could in order to beat Jerry to it.
[ ; c. 1900
Also,beat to the draw or punch. React more quickly than someone else. For example, The new salesman tried to serve one of my customers, but I beat him to the draw and Bill was determined to get there first and beat everyone else to the punch. The variants imply aggression to get ahead, draw alluding to the drawing of a pistol and punch to hitting with the fists.
[ Second half of 1800s