If you know that’s town or county that it was located in, I would recommend pursuing state licensing offices for records. I’m not familiar with what a print shop might need for licenses but they almost certainly would have had to pay taxes or have gone to local courts to deal with any disputes.

Another route would be looking at local papers, most have a older additions digitized on their websites or digitized thru local universities or museums. If you had a timeframe and general location you could poke thru digitized collections with a few key words. There might be old advertisements or announcements for the business opening?

Local historical societies also tend to have random stuff squirreled away somewhere so you could reach out to them too for info, research, or even fresh eyes with a baseline familiarity of the local history that might think of an angle you didn’t consider.