How can I automatically delay the triggering of a task (or tasks) in an incident template?

I'm trying to find the best way to handle tasks that need to happen according to a particular schedule. For instance - in one of our (Incident) templates when the request is submitted there are a number of tasks that need to be done immediately. However there are a few tasks that cannot and should not be started until a certain number of days has passed.

I've created a task that I'm using as a parent dependency for the delayed task, but it requires someone to manually close it after the waiting period before the owner of the delayed task can begin their task work. I tried creating the parent task with a closed status but that defeats the purpose of the delay and allows the delayed task owner to begin their task prior to the end of the delay period.

Is there a way to automatically delay the triggering of a task or tasks by say 30 days or 60 days without me having to close a dependent task manually?