In the first of five rounds in Marrakesh, McCook signed for six birdies but also dropped six shots in two holes as she followed an 8 at the second with a 6 at the third at Amelkis Golf Club.
That left McCook, winner of both the Irish and Welsh Open Stroke-Play Championships this year, having to settle for a three-over-par 75 to sit joint 68th out of 115 card hopefuls.
German-based Rachael Taylor fared best of the Scots with a one-under 71 on the same layout, leaving her joint 25th on a day when India’s Astha Madan set the pace with a bogey free 65.
Alison Muirhead, who has also entered as an amateur, is in a share of 43rd after a 73, one shot less than Laura Murray, Heather Stirling and Jane Turner, while Vikki Laing sits alongside McCook.
Ireland’s Leona Maguire, a former women’s amateur world No 1, is handily placed after an opening 68 while England’s Bronte Law and Swede Linnea Strom had matching 70s to also lie in the top 15.
Elsewhere, Englishman Roger Chapman secured his first Staysure Tour title in more than six years after beating Phillip Price of Wales in a play-off at the MCB Tour Championship in the Seychelles.
Chapman, a two-time senior major winner in 2012, closed with a 63 in the final event of the 2018 season before claiming victory in style in the sudden-death shoot-out with an eagle-3 at the 18th.
Another Englishman, Paul Broadhurst, picked up the John Jacobs Trophy for the second time in three years after topping the Order of Merit, finishing ahead of Price with Gary Orr, a two-time victor on the circuit, ending up in eighth position.