The first golf in America can arguably be traced back to the 18th century (the 1700s) and Charleston SC seems to be the earliest spot.
However, golf in America that early was almost never self sustaining for a number of reasons.
Those over here who created the first golf and courses in America that early did not stay in this country and those early courses and golf over here were not on-going for that reason. Also perhaps for another rather simple but practical reason golf was not self sustaining over here that early---eg when those early GBer came over here and created those very early rudimentary courses and played on them they brought their own balls and impliments with them from GB and when they left they took them home with them.
One could not exactly play golf over here if there were no balls and impliments over here to play with and in those very early days no one over here made them.
Golf courses that have been on-going did not begin in this country until around the 1880s.
Furthermore, the inland golf courses over here from about the 1880s up until the first decade of the 20th century essentially looked like steeplechases courses or adaptations of other features to do with horse sport---at least their hazard features did.
Is it any wonder they looked like that early on? Most of those early features probably were copies of steeplechase features or even adaptations of actual horse jumping features.
A thorough photographic review of courses over here in that early era make that fact virtually undeniable.