A manufacturing method is provided during which a preform component for a turbine engine is provided. The preform component includes a substrate and a locating feature at an exterior surface of the substrate. An outer coating is applied over the substrate. The outer coating covers the locating feature. At least a portion of the preform component and the outer coating are scanned with an imaging system to provide scan data indicative of a location of the locating feature. A cooling aperture is formed in the substrate and the outer coating based on the scan data.