Yes, you can select a different date to start your pack at the time of purchasing the pack.
You can extend this date further even after pack purchase. However, you must do this before your first cult class or check-in. The extension is allowed only till 30 days of your originally selected pack purchase date and you can make this change twice.
In case of session based packs like cult transform and PT, the start date is determined by the day of your first session.