Invalid outbound configuration Error:

This "Invalid outbound configuration" error occurs when you try to make an outbound call in Amazon Connect but the necessary configuration is missing. To resolve this issue, you need to:

1. Ensure your Amazon Connect instance is enabled for outbound calling at the instance level.

2. Associate a phone number with your outbound queue by:

• Logging into the Amazon Connect admin website (https://yourinstancename.my.connect.aws/)
• Navigate to "Routing" and then "Queues"
• Select the queue you're using for outbound calls
• In the "Settings" section, under "Outbound caller configuration," select a valid phone number from the "Outbound caller ID number" dropdown
• Save your changes

3. Verify that your user account has the necessary permission "Contact Control Panel (CCP) - Make outbound calls" in your security profile.

4. Check that your routing profile has a default outbound queue configured, and that this queue has an outbound caller ID number assigned to it.

Note that if you're trying to use a toll-free number as your outbound caller ID, it might cause issues as telecom regulators might flag it as spam. It's better to use a Direct Inward Dialing (DID) number that you've configured in your Amazon Connect instance.
Sources
Contact Control Panel (CCP) Issues - Amazon Connect
Troubleshoot outbound call issues in Amazon Connect | AWS re:Post
Troubleshoot outbound caller ID issues in Amazon Connect | AWS re:Post

Correct, the short of it is that the routing profile you user has needs to have an outbound queue associated with it and that queue needs to have a phone number associated to it.