Unlike with the CLI commands, there is no shorthand way to create a CloudFront distribution with a CloudFormation template without specifying the distribution config parameters. I will, however, only add the essential parameters in this recipe:

1. Start the template with the template version and a description (optional).
2. Create a resource of the type AWS::CloudFront::Distribution:

Resources:
  MyCloudFrontDistribution:
    Type: AWS::CloudFront::Distribution
    Properties:
      DistributionConfig:
        Origins:
        - DomainName: quizzer.cloud.s3.amazonaws.com
          Id: myS3Origin
          S3OriginConfig:
            OriginAccessIdentity: ''
        Enabled: 'true'
        Comment: 'CloudFront Distribution for S3 Bucket'
        DefaultRootObject: index.html
        DefaultCacheBehavior:
          TargetOriginId: myS3Origin
          ForwardedValues:
            QueryString: 'false'
            Cookies:
              Forward: none
          ViewerProtocolPolicy: allow-all

3. Add an Outputs section to return the CloudFront distribution ID and the CloudFront domain name:

Outputs:
  CloudFrontDistributionId:
    Value: !Ref MyCloudFrontDistribution
    Description: 'CloudFront distribution id'
  CloudFrontDomain:
    Value: !GetAtt MyCloudFrontDistribution.DomainName
    Description: 'CloudFront distribution domain name'

4. Execute the stack, using the create-stack command.

It will take some time for the distribution to be created. You can check the status by using the describe-stacks command. Once it has completed, you will get a response with the Outputs section, as follows:

5. Execute the CloudFront domain name in a browser, and verify whether the S3 static website has loaded: