Use CloudFront Proxy to access Lambda APIs

Thanks! It helped. In case it would help anyone, here’s the updated json. I still have to check some things but for now it works.

{
    "CloudFrontDistribution": {
        "Type" : "AWS::CloudFront::Distribution",
        "Properties" : {
            "DistributionConfig" : {
            "DefaultRootObject" : "",
            "Enabled" : true,
            "DefaultCacheBehavior" : {
                "AllowedMethods" : ["GET", "HEAD"],
                "CachedMethods" : ["HEAD", "GET"],
                "ForwardedValues" : {
                    "QueryString" : true
                },
                "MinTTL" : "0",
                "TargetOriginId" : "MY_SERVICE-${opt:stage}-serverlessdeploymentbucket-s3.amazonaws.com",
                "ViewerProtocolPolicy" : "allow-all"
            },
            "CacheBehaviors" : [
                {
                    "AllowedMethods" : ["DELETE", "GET", "HEAD", "OPTIONS", "PATCH", "POST", "PUT"],
                    "CachedMethods" : ["HEAD", "GET"],
                    "ForwardedValues" : {
                    "QueryString" : true
                    },
                    "MinTTL" : "0",
                    "PathPattern" : "*",
                    "TargetOriginId" : "MY_FUNCTION-${opt:stage}-api-gateway",
                    "ViewerProtocolPolicy" : "allow-all"
                }
            ],
            "Origins" : [
                {
                "CustomOriginConfig" : {
                    "HTTPSPort" : "443",
                    "OriginProtocolPolicy" : "https-only"
                },
                "DomainName" : {
                    "Fn::Join": [
                        "",
                        [
                            {
                                "Ref": "ApiGatewayRestApi"
                            },
                            ".execute-api.us-west-2.amazonaws.com"
                        ]
                    ]
                },
                "Id" : "MY_FUNCTION-${opt:stage}-api-gateway",
                "OriginPath" : ""
                },
                {
                "DomainName" : {
                    "Fn::Join": ["", [{"Ref": "ServerlessDeploymentBucket"}, ".s3.amazonaws.com"]]
                },
                "Id" : "MY_SERVICE-${opt:stage}-serverlessdeploymentbucket-s3.amazonaws.com",
                "OriginPath" : "",
                "S3OriginConfig" : {}
                }
            ],
            "PriceClass" : "PriceClass_100"
            }
        }
    }
}