Aditi, who had finished fourth at the Tokyo Olympics, scored four birdies against three bogeys and three of those birdies came in a fine stretch between 10th and 14th.
The Indian is four shots behind the three co-leaders -- World No. 1 and Olympic gold medallist Nelly Korda, Korean Sei Young Kim and Sweden's Madelene Sagstrom.
The trio produced a matching five-under 67 each in the opening round.
Three-time Ladies European Tour winner, Aditi, who qualified for her 19th Major through the Final Qualifying at Panmure Golf Club, showed a lot maturity and patience, so crucial while playing the Links.
"I played good today, I think I drove the ball well and that was definitely a key to scoring well. I started off good with a birdie on the first as I hit a 7 iron to 10 feet and holed the putt," Aditi said.
"Had bogeys on 6th and 7th as both drives ended in the pot bunkers, and after that I realised that mistakes are there on this course to be made, it's just about staying patient and keeping composure and I think I did that well today, even though I had two bogeys I came back from it.
"I had a nice hole out bunker shot on the 10th but the bunker shot was totally about 7 yards so it was like a 20 footer from the bunker. But yeah that was nice to hole that out."
Aditi, who started the tournament with a birdie turned in one-over after bogeys on sixth and seventh. After the turn she found some rhythm and it helped.
"Then I got into a good rhythm and hit a 5 iron to 12 feet on 13th hole and holed that putt. On the 14th I hit a 9 iron which almost went in the hole I think ended up 4 feet past and I holed that putt for a birdie," she said.
"Obviously finishing stretch at Carnoustie is pretty difficult but I had a 3 wood coming in to the last 3 holes, managed pars on 16, 17 but bogeyed 18.
"But it was still a good round, I think. The 18th was the second toughest hole on the course. Obviously a dropped shot is never good but I think it was okay."
Major winner Korda made eight birdies on her way to a share of the lead.
Four players are one stroke back on four-under-par 68 including 2018 Women's Open champion Georgia Hall, who was joined on four-under-par by Scottish amateur Louise Duncan who carded a round of 68 which included an eagle on 14.
American Andrea Lee and 2021 US Women's Open champion Yuka Saso are also tied for fourth place.