This could just as easily be related to increased infections among young people at this time. You have no reason to pin this specifically on vaccination.
But yes, one way to answer that question definitively would be to do a cohort study on conception rates. Split the data by vaccine status. This can't be done because public health agencies systematically refuse to do this sort of study, nor do they expose the necessary raw data. They don't want anyone being able to answer these sorts of questions. Most data that is available has to be forced out via FOIA requests and the courts.