Chance favors the prepared mind, said Louis Pasteur. Sometimes, significant breakthroughs occur when we creatively integrate new information, leading to a creative insight or an Aha! moment, while at other times when we fail to use a clue, we remain stuck in our habitual thinking patterns. In this study, we hypothesized that the brain's transient oscillatory states would characterize its receptivity or preparedness for such insights. We conducted a real-time brain-state-dependent cognitive stimulation experiment during insightful problem-solving. We showed that participants were more successful in utilizing clues and experienced more Aha responses when these clues were presented at the spontaneously up-regulated state of right temporal alpha oscillation, as opposed to the down-regulated state. Furthermore, we observed an inverse correlation between the coupling of alpha oscillation phase and gamma oscillation power and the frequency of insight. These results shed light on the neural mechanism underpinning the brain's receptivity to integrate upcoming semantic information, emphasizing the pivotal role of dynamical brain oscillations in the Aha! experience.