Had a similar experience when rebuilding Pioneer Park in Lincoln, NB about 1989. When they started dozing, I spotted a bramble ball, last made around 1900 and this course was built in 1914 (Tucker). So, if that guy lost the ball on opening day, it was probably a 15 year old golf ball, maybe more. Golfers were more frugal then, I guess. I kept the ball for years, and may still have it, but recall it falling apart after a while, and it was in two barely connected pieces when I picked it up.
The more common artifacts to find when building courses are old coke bottles and the like, and sometimes arrowheads, although that is far less common than when I started in 1977. Back in 1999 or so, I found some Dutch dishes/pottery on a golf course site west of Ft. Worth, near what had been an old homestead. In pretty good shape, too.
In Atlanta, we found some old civil war minnies, a cannon wheel and a few other things on a site right in the path of Sherman's march to Atlanta.