A method is provided for forming a thermoplastic structure. During this method, a substrate is provided. The substrate includes a substrate thermoplastic and a plurality of substrate fibers disposed within the substrate thermoplastic. The substrate fibers are arranged in a substrate pattern. A first layer is deposited on the substrate using an automated fiber placement device. The first layer includes a first layer thermoplastic and a plurality of first layer fibers disposed within the first layer thermoplastic. The first layer fibers are arranged in a first layer pattern that is different than the substrate pattern. A blank is stamped into the thermoplastic structure. The blank includes the substrate and the first layer where the first layer thermoplastic is consolidated with the substrate thermoplastic.