The earliest that I know of from advertising and catalog reprints is 1941. The 1941 catalog reprints depict the 48BG, 58BG, 68BG, 48BGH, 58BGH and 68BGH sheaths as having the acorn and oak leaf (A&OL) pattern on their sheaths.
It is possible that some of the other 1941 offerings had A&OL sheaths, but the catalog pages don't show any details on any of the other few sheaths depicted. The sheaths that can be seen all appear to be plain, with 1 knife/axe combo having a stamped pattern around the edge and 1 "upgrade" taco sheath with lacing along the edge and a tooled pattern.
It is also possible that the A&OL pattern popped up sometime during the 1936 to 1940 period.
Part of the problem is that many of the sheaths from that era have not survived. All of the sheaths that I have with my known 1936 to 1940 knives do not have the A&OL are either plain or have what I call "the flower pattern".