The integration of generative artificial intelligence (GenAI) into education presents a critical paradox: does it act as a temporary "cognitive crutch" that enhances immediate performance at the cost of long-term skill, or can it serve as a "cognitive gymnasium" for enduring learning? Cross-sectional studies have been unable to resolve this tension. Adopting a social constructivist perspective, this longitudinal study investigates the dynamic process through which students' skill in querying AI fosters creative capacity over time. We conducted a two-wave study with university students, measuring their creative performance immediately after a GenAI-supported task (Time 1) and again one week later (Time 2). Results from a moderated mediation model revealed a distinct temporal shift. At Time 1, AI inquiry quality influenced immediate creativity through two parallel paths: a strong direct effect and an indirect effect via critical thinking. However, at Time 2, the mechanism transformed entirely: the direct effect vanished, and AI inquiry quality influenced delayed creativity solely through the enduring indirect pathway of critical thinking. Crucially, this pathway of internalization was exclusively available to students with a high learning-goal orientation. This finding demonstrates that the cognitive benefits of the engagement were not automatic but were sustained over time through a motivated process of knowledge construction. This study contributes a dynamic model of AI-supported skill acquisition, highlighting that lasting creative gains are not a function of AI use alone, but of a motivated, constructivist engagement. We provide clear evidence that pedagogies must shift from teaching how to get answers from AI to fostering the inquiry skills and learning mindsets that drive internalization.