The VA reports a typical turn-around time of 30 days between certification and payment. In our experience, that time-line can vary. Some tuition payments are received in less than a week, some take several months. It can depend on the time of year and whether the certification was pulled for manual processing (which may happen if there’s a question about the cert or if a revision is submitted.)
It is our understanding that BAH payments begin roughly 30 days from the cert date, but not before the start of term. BAH payments, if sent after the start of term, should be retroactive to the first day of enrollment.