Coughlin, who won the Scottish Open in 2024, compiled eight birdies and two bogeys on a links course that didn't play like normal due to Europe's recent heat wave.
But it was a day to forget for Australia's Minjee Lee, who signed for a 13-over 85 including seven bogeys and three double-bogeys, leaving the multiple major winner in a tie for second-last place.
Co-leader Coughlin admitted it was tough going for everyone.
"It was pretty difficult out there," said the American.
"I've not ever really played it when it's been this firm, especially off the tee, so quite a few different things off the tee than normal where I used to be able to hit the driver a lot of places."
Shin, who started on the back nine like Coughlin, posted seven birdies on the day - including birdies at her first three par-5s.
"It's playing a little shorter than the years past when it was quite wet out here," Shin said.
"And the fact I was able to reach the par-5s and take advantage of making the birdies there, and having a few 58-degree (wedges) coming into the green helped.
"I was able to get my ball within 15 feet and when I did have the chance for birdie, I did make it. So it was a good day."
Korea's A Lim Kim sits one shot behind at 67 while Sweden's Lisa Pettersson (69) posted the day's only other sub-70 score in the 144-golfer field.
World No. 1 Nelly Korda posted a 72 to share 14th place after one round.
Playing in the same group as Korda, defending champion Lottie Woad of England got off to a poor start with a double bogey on No. 3 and a bogey on No. 4 before settling down for a 74.
Major winners Grace Kim and Hannah Green (both 74) were the best of the Australian contingent in a tie for 33rd, two strokes ahead of Cassie Porter.
Scottish-born Karis Davidson and Robyn Choi both shot 76.
- with AAP
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--Field Level Media
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