I have this business card that I just found from my grandfather who practiced as a pediatrician in Cuba in the 1950s and early 1960s.
Great question! This was quite a common style of business card typeface and lettering. Goudy did a design in this style called "Copperplate Gothic" which is probably the best known, but that was based on earlier ones. Fonts in this style include "Steelplate Gothic" and Sackers Gothic and Blair.
A lot of typefaces in this style had small serifs on the end of the letter. From your picture it's a little hard to be sure if the fonts used do, but I think they do.
Copperplate Gothic itself is available digitally, you probably have it on your computer now but the early digitization got used a ton and feels a bit 90s because of it-you might be best off using a more obscure font in the style to seem a bit less cheap. President was a French take on the style but that feels a bit wonky. Right now I don't have a specific great modern font in the style to recommend but that should get you started on knowing where this comes from.