TePaul,
It is interesting but doesn't really answer your question. It was difficult work and on another map history site, they wrote that the biggest advances were during times of War, specifically the Civil War, where generals went all high tech, using railroads for supply, balloons for recon and maps to fight the war.
Around Atlanta, I have seen some old war maps and the southern ones, with home field advantage seemed much better, but it is acknowledged that generally, the north had better mapping skills. I have told the story, but we overlaid an old Union march route map over our golf course maps (we had to do a lot of work to get it to scale) and when we were clearing trees, right where it said the cannons crossed Pumpkinvine Creek, we found a natural rock bridge and waterfall!
Other histories of maps say the first US mapping was around cities, and then of course the American West. Golf courses were probably down the priority list, so seeing references to them in the early 1900's probably made sense.
Just looking at old Scottish courses, I don't recall too many maps with contour lines, if any drawn in the 1800's. But golf grew in America after topo mapping got into full swing, and generally had a more scientific path than early courses in GBI so the timing was perfect for golf courses to use them. I imagine a course like the first NY muni might have inadvertantly been the first to use good topos, since they may have already been done for the cities. If not those, then perhaps a develoment course (like Merion) where the developer could recoup the cost of the maps more readily than a financially strapped golf course. Of course, there just might have been some rich guy interested in having maps of his property and having a golf course, too.
In any case, it is an interesting subject and maybe going back through that compilation of golf course maps thread might yield and earlier date than suggested in posts above.