No, there's not a minimum time period required, and technically your first payment is at closing as part of your closing costs. This will be shown on your settlement statement as a prepayment as Heather mentions.
A typical but not always is for your payment to be due on the first of the month. If you were to close in September, you would prepay a prorated interest payment from the date of closing through October 1 with the next payment due November 1.
Of course some lenders may offer a different due date or other options and the prepayment adjusted accordingly. Your loan officer should be able to explain what their policies are and any options they may have to offer even before heading to the closing table.
Hope that helps.