As a shipper, you can setup when your summary emails get sent to you. You can always go to the track tab in Momentum to get the tracking number as soon as the label is created.
Your customers, on the other hand, will receive email alerts based on when the package travels throughout the shipping process. For UPS for example, packages start tracking from around 9:00 pm all the way to 2:30 am. So for UPS shipments, your customer will receive the first email within that timeframe.
The number of email alerts your customer receives depends on the selections you make at the email notification section. See here for more information.