I am unable to create CloudFront distributions

The error message you're encountering is a common issue when trying to create CloudFront distributions. Even though you've already been using other AWS services like EC2, S3, and Lambda successfully, CloudFront specifically requires an additional verification step.

To resolve this issue, you should:

1. Open a case with AWS Support through the AWS Support Center if you haven't already done so. Since you mentioned case #176239586300554 from seven days ago, it seems you've already taken this step.

2. Make sure your case is under the "Account and billing support" category, which is available free of charge.

3. In your support case, include the exact error message you're receiving.

4. You might also want to request a Service Quota increase specifically for "CloudFront Distributions" and "Web Distributions per Account" as the quota type.

This verification requirement is a security measure implemented by AWS and applies even if your account has been verified for other services and you have a valid payment method. The verification process for CloudFront is separate and additional.

Since it's been seven days since you opened your case, I would recommend following up on your existing case or opening a new one to expedite the process. Sometimes, AWS Support might need additional information from you to complete the verification.
Sources
Can not create Cloudfront distribution | AWS re:Post
AWS account needs to be verified before you can add new CloudFront resources | AWS re:Post
CloudFront Verification | AWS re:Post