Currently when users make a recurring contribution or a self-service pledge - the first payment is done immediately and the payment schedule is set based on the current day of the period.
Back-office (admin-entered) pledges support this functionality already - so adding it to self-service mode will be pretty easy. For recurring contributions we'll need to investigate what directives are supported by the recurring processor (i.e. can you give them a start date, can you submit a recurring payment request w/o making the initial payment at the same time).
Some background for this is here: