The textile industry had a long tradition of using numeric controlled weaving looms. The Jacquard machine with punched cards control was invented 1804.
Jacquard's invention had a deep influence on Charles Babbage. In that
respect, he is viewed by some authors as a precursor of modern
This portrait of Jacquard was woven in silk on a Jacquard loom and required 24,000 punched cards to create (1839). Only a small part of the large portrait.
In 1898 Joseph Arnold Gröbli (1850-1939), the eldest son of Isaak Gröbli, developed the fully automated embroidery machine controlled by a punch card reader. See Wikipedia.
So a numeric controlled embroidery machine was available 60 years before the Apollo Mission. Many thanks to DrSheldon for providing the search string "Swiss Embroidery Loom".
But the design of a control program for the machine was pure manual work only, no CAD, no color graphic raster display were available during the early sixities. No editor with copy and paste functionality could be used.
Hopefully they got a combination of a paper tape reader with a paper tape punch to copy a part of a tape to a new one.