Don Moe arrived on the local golf scene in 1925 when he beat Doug Nicol, 7 & 6, in the final of the Portland City Amateur Championship. He became even better known when he finished runner-up in the Oregon Amateur to Rudie Wilhelm in 1927. Moe broke through with his first
Oregon Amateur win in 1928, then finished second in the same tournament to Doc Willing in 1929 and Johnny Robbins in 1933. Moe later won the Oregon Amateur in 1937.

Playing out of Eastmoreland Golf Course and later Alderwood Country Club, Moe had strong rivalries with such top Northwest players as Doc Willing, Frank Dolp, George Von Elm, Harry Givan and Jack Westland.

Moe's greatest successed came in the Western Amateur, which he won in 1929 and 1931. (Between 1926 and 1931, Northwest golfers won the Western Amateur five of six times, with Frank Dolp in 1926 and 1928, and Bon Stein in 1927.) When he took the title in the 1929 Western Amateur in Kansas City, Moe was selected to the USGA's Walker Cup Team, the ultimate achievement in amateur golf.