The automation of machine tool control began in the 1800s with cams that "played" a machine tool in the way that cams had long been playing musical boxes or operating elaborate cuckoo clocks. Thomas Blanchard built his gun-stock-copying lathes (1820s-30s), and the work of people such as Christopher Miner Spencer developed the turret lathe into the screw machine (1870s). Cam-based automation had already reached a highly advanced state by World War I (1910s).
However, automation via cams is fundamentally different from numerical control because it cannot be abstractly programmed. There is no direct connection between the design being produced and the machining steps needed to create it. Cams can encode information, but getting the information from the abstract level of an engineering drawing into the cam is a manual process that requires sculpting and/or machining and filing. At least two forms of abstractly programmable control had existed during the 1800s: those of the Jacquard loom and of mechanical computers pioneered by Charles Babbage and others. These developments had the potential for convergence with the automation of machine tool control starting in that century, but the convergence did not happen until many decades later.
