as far as I know Nintex can't monitor the new mail event. However you can do so with Microsoft Flow if you're using Exchange Online in Office 365.
Would that be an option for you?
You can use the When a new email arrives trigger to create a flow that runs when one or more of these email properties match criteria you provide, A good starting point for flow would be : Run flows based on email properties. | Microsoft Flow
Do you have also SharePoint on-premise? Maybe you could approach that the other way round:
But I have no idea about the background and the architecture of your environment, sooo... Can't tell if that is feasible