UPDATE: Your engine serial 3691623 is NOT in the records for the North American aircraft engine distributor. I checked the paper records again, and I see now that I originally mis-read the listing notes.
So it's safe to say that it was instead produced as a Ski-Doo, Sea-Doo, or other non-aircraft variant of the 503 engine type.
But I am pretty sure we can conclude that it was produced early 1987 to about mid-1987, as during serial production it falls between engines 3682922 and 3693155, which are both listed as received in shipments June/July 87 on the North American distributor's notes (see pic)