Create incident but wait until person is on-call to alert

I know that an alert directed to a service (lets say Cloudwatch for example) will not create an incident if someone isn’t on call in the escalation policy that’s attached to the service. But is there any “creative” way around it? I’ve been tasked to figure out how to have low priority (ones that are okay to not wake someone up but to have visibility when they start their shift) incidents queue up and then alert when a person goes on call.

Did you look at “Support Hours” feature on each service?