In recent years, generative AI (GenAI) in educational settings has become ubiquitous in university students' daily lives, despite its potential to induce over-reliance, metacognitive disengagement, and diminished learning when used unrestrictedly. While most prior research has focused on how to pedagogically scaffold its usage, the question of when to allow off-the-shelf GenAI remains understudied and lacks pedagogically grounded empirical investigation. We treat access timing itself as a form of implicit scaffolding and operationalize it through a reinforcement learning (RL) agent that decides when students should access GenAI, with a reward function grounded in metacognitive theory, cognitive load theory, and productive failure. In a mixed-methods controlled lab study with N=105 higher education students, we compared the agent's effect on learning gains and metacognitive engagement to unrestricted and fully restricted use. Results show that strategically timed GenAI access under the reinforcement learning condition improved objective post-test performance and metacognitive accuracy compared with unrestricted access, while reducing task errors and time on task relative to complete withholding, thus outperforming both approaches without the need for explicit metacognitive prompts or structured scaffolding. However, no between-condition differences emerged on self-reported metacognitive awareness. Overall, timing of GenAI access therefore is a tractable, theoretically grounded, and scalable pedagogical strategy that improves over completely unrestricted and withheld access, compatible with off-the-shelf tools and potentially low adoption barrier. This opens up a new research area that explores how access timing can be facilitated by educators and implemented in human-AI learning system design.