At this time, we do not have any functionality that allows for retroactively starting a subscription, or backdating subscription start dates. An alternative would be to just line up the next bill date with what it would have been had the subscription started on the date you want to backdate to.
Read more on aligning the next billing date with the Postpone Subscription feature our docs here: https://docs.recurly.com/docs/postpone-subscription#section-backdate-a-subscription