In-universe, there are a several female chief engineers that pre-date Lieutenant Commander MacDougal serving on the Enterprise-D under Captain Picard in 2364;
Lieutenant Commander Caitlan Barry served as Chief Engineer aboard the original USS Enterprise under Captain Pike sometime around 2254.
Number One twisted in midair and angled her body so she caromed off the side wall of the null-G ball court using her right leg to push her back toward the center. Chief Engineer Caitlin Barry had anticipated the move and shot in front of the exec, body-blocking her away from the ball. The collision of bodies sent them careening off in opposite directions, but Caitlin had managed to backhand the ball, slapping it toward the catch-trap goal in Number One’s end of the court. As Number One somersaulted in the air to land with her feet against the end wall under Caitlin’s goal, she saw the ball hurtle straight through the catch trap and in. The Scoreboard honked and racked up the three points for the chief engineer.
Commander Jett Reno was Chief Engineer of the USS Hiawatha sometime around 2257.
Commander Jett Reno was Chief Engineer of the U.S.S. Hiawatha when it crash-landed on an asteroid. She transferred to the U.S.S. Discovery after they were rescued.
Lieutenant Bexx was the Chief Engineer on the USS Hunley under Captain Linneus sometime around 2270circa 2275.
Harriman moved through Hunley’s engine room, waiting anxiously for word from Lieutenant Bexx. He paced back and forth behind the chief engineer, trying not to disturb her as she worked at an environmental-control console, but—“Anything?” he asked, stopping beside her. From an intellectual standpoint, he understood the requirements of command, and the need to allow people to do their jobs, but however much time they had, he knew that it must be running out quickly.