Colin,
Here is a link to an article by Devereux Emmet on private courses. The article includes pictures of the Kahn estate course. The article is dated December 1919. Judging by the pictures, the course looks well established by 1919.
http://library.la84.org/SportsLibrary/GolfIllustrated/1919/gi123o.pdfThe Kahn estate was purchased in 1914 and it took two years to bring in enough dirt to make the Kahn estate one of the highest points on Long Island.
C.B. Macdonald also writes about the Otto Kahn course in
Scotland's Gift Golf on page 305:
"I tried to deter Otto Kahn from building 18 holes, but he thought he would have a fine lawn in front of his beautiful Long Island House. Of course, that in itself is worth while"
There is another thread or two on this subject which included an article as early as 1917 mentioning Macdonald building a private links for Otto Kahn. However, at the time Kahn owned two separate estates, both with 18 hole courses. Considering I have never seen an attribution for Macdonald building a course at Cedar Court, I strongly believe this article was referring to Oheka.
Sorry, I don't have an exact date, but maybe this can narrow down your search.
Bret