Host club member Scott, the younger brother of world No 7 Sandy, took full advantage of the early starters being out before a breeze turned into a gale to card a bogey-free four-under-par 67.
That was the best score by three shots for most of the day until Englishman Dyer, who played in last month’s Walker Cup in Florida, picked up five birdies as he came home in 32 to sign for a 68.
US-based English player Frank Kennedy and Irish duo Luke O’Neill and Max Kennedy were the only other players to break par as they opened with 70s in the battle to secure 64 spots in the match-play stage.
Scott, who is set to follow in his big brother’s footsteps by heading to Texas Tech University later this year, birdied the seventh going out before adding gains at the 10th, 15th and 18th on his inward journey.
“We were pretty lucky,” he said of being out early. “The first few holes were windy, but it’s now blowing a gale.
“I managed to get through the first seven holes in one-under, which is really good into that breeze, and 67 is my best score off the black tees.
“I don’t want to get too ahead of myself, though, because anything can happen with that wind. I’m out at midday tomorrow and I expect the wind to pick up.”
Scottish champion George Burns (Williamwood) and Suffolk-based Gregor Tait (Aldeburgh) were next best among the home contingent with 71s late in the day.
John Paterson (St Andrews New) and Matt Clark (Kilmacolm) are also to the fore after matching 72s, with Murrayfield’s Andew Ni in the top 20, too, following a 73.
Other host nation players to make promising starts included 57-year-old Dunnikier Park man Derek Paton, who was six-over after five before coming home in three-under for a 74.
“I must be one of the oldest to play in the event,” he said. “But I’m playing well, so age really is just a number.”