Automation with DELAY AT LEAST

There should be a filter with the automation that allow message to be sent event after the due time. Let’s say, I want to make sure our guest received some information one week in advance to their trip. However we sometimes have last minute booking. Thus, when the message used for checking information is set to 7 days in advance, those with last minute booking do not receive it. We need a parameter allowing the message to be sent AT LEAST 7 days prior to arrival, thus if a booking appears after the delay, ie 3 days before arrival, they would still receive the information automatically.