To automatically connect input sources on startup, open the Input Strip from the View menu (or using a toolbar shortcut). See Multiple Input Sources for details on setting up the Input Strip.
Once your input device is connected to one of the input slots, right-click the thumbnail and select Auto-connect:
Auto-connect setting in the Input Strip
You can set multiple sources to auto-connect on startup and save these settings in your layouts. Remember to save the layout after making changes.
Please note that Input Strip (and auto-connect) functionality is only available in the Pro version of OmniScope.