aws api gateway with step function execution

cfn.yml

AWSTemplateFormatVersion: 2010-09-09
Description: My API Gateway and Lambda function

Parameters:
  apiGatewayName:
    Type: String
    Default: my-api
  apiGatewayStageName:
    Type: String
    AllowedPattern: "[a-z0-9]+"
    Default: call
  apiGatewayHTTPMethod:
    Type: String
    Default: POST

Resources:
  apiGateway:
    Type: AWS::ApiGateway::RestApi
    Properties:
      Description: Example API Gateway
      EndpointConfiguration:
        Types:
          - REGIONAL
      Name: !Ref apiGatewayName

  apiGatewayRootMethod:
      Type: "AWS::ApiGateway::Method"
      DependsOn:
        - SPIStateMachine
      Properties:
        ResourceId: !GetAtt apiGateway.RootResourceId
        RestApiId: !Ref apiGateway
        AuthorizationType: "NONE"
        HttpMethod: "POST"
        Integration:    
          Credentials: !GetAtt ApiGatewayStepFunctionsRole.Arn
          IntegrationHttpMethod: "POST"
          PassthroughBehavior: "NEVER"
          IntegrationResponses:
            - StatusCode: '200'
              ResponseTemplates:
                application/json: |
                  { "executionId": "$input.json('executionArn').split(':').get(7) }
          RequestTemplates:
            application/json:
              Fn::Sub:
              - '{"input": "$util.escapeJavaScript($input.json(''$''))","stateMachineArn":"${arn}"}'
              - arn:
                  Ref: SPIStateMachine
          Type: "AWS"
          Uri:
            Fn::Join:
            - ''
            - - 'arn:aws:apigateway:'
              - Ref: AWS::Region
              - ":states:action/StartExecution" 


  apiGatewayDeployment:
    Type: AWS::ApiGateway::Deployment
    DependsOn:
      - apiGatewayRootMethod
    Properties:
      RestApiId: !Ref apiGateway
      StageName: !Ref apiGatewayStageName

  ApiGatewayStepFunctionsRole:
    Type: AWS::IAM::Role
    Properties:
      Path: !Join ["", ["/", !Ref "AWS::StackName", "/"]]
      AssumeRolePolicyDocument:
        Version: 2012-10-17
        Statement:
          - Sid: AllowApiGatewayServiceToAssumeRole
            Effect: Allow
            Action:
              - 'sts:AssumeRole'
            Principal:
              Service:
                - apigateway.amazonaws.com
      Policies:
        - PolicyName: CallStepFunctions
          PolicyDocument:
            Version: 2012-10-17
            Statement:
              - Effect: Allow
                Action:
                  - 'states:StartExecution'
                Resource: !Ref SPIStateMachine
        - PolicyName: DescribeStepFunctionExecutions
          PolicyDocument:
            Version: 2012-10-17
            Statement:
              - Effect: Allow
                Action:
                  - 'states:DescribeExecution'
                Resource: "*"

  StateExecutionRole:
      Type: AWS::IAM::Role
      Properties:
        AssumeRolePolicyDocument:
          Version: '2012-10-17'
          Statement:
            - Effect: Allow
              Principal:
                Service:
                  - !Sub states.${AWS::Region}.amazonaws.com
              Action:
                - 'sts:AssumeRole'
        Policies:
          - PolicyName: "StatesExecutionPolicy"
            PolicyDocument:
              Version: "2012-10-17"
              Statement:
                - Effect: "Allow"
                  Action: "lambda:InvokeFunction"
                  Resource:
                    - !GetAtt lambdaFunction.Arn

  lambdaFunction:
    Type: AWS::Lambda::Function
    Properties:
      Code:
        ZipFile: |
          def handler(event,context):
            return {
              'body': 'Hello there {0}'.format(event['requestContext']['identity']['sourceIp']),
              'headers': {
                'Content-Type': 'text/plain'
              },
              'statusCode': 200
            }
      Description: Example Lambda function
      FunctionName: "myfunction"
      Handler: index.handler
      MemorySize: 128
      Role: !GetAtt LambdaRoleForRuleExecution.Arn
      Runtime: python3.8

  LambdaRoleForRuleExecution:
    Type: AWS::IAM::Role
    Properties:
      RoleName: !Sub ${AWS::StackName}-lambda-role
      AssumeRolePolicyDocument:
        Version: '2012-10-17'
        Statement:
          - Effect: Allow
            Action: 'sts:AssumeRole'
            Principal:
              Service: lambda.amazonaws.com
      Policies:
        - PolicyName: WriteCloudWatchLogs
          PolicyDocument:
            Version: 2012-10-17
            Statement:
              - Effect: Allow
                Action:
                  - 'logs:CreateLogGroup'
                  - 'logs:CreateLogStream'
                  - 'logs:PutLogEvents'
                Resource: 'arn:aws:logs:*:*:*'
          PolicyName: lambda

  SPIStateMachine:
      Type: "AWS::StepFunctions::StateMachine"
      Properties:
        StateMachineName: "my-state-machine"
        RoleArn: !GetAtt StateExecutionRole.Arn
        DefinitionString: 
          Fn::Sub: 
          - '{"Comment":"A Hello World example of the Amazon States Language using an AWS Lambda function","StartAt":"HelloWorld","States":{"HelloWorld":{"Type":"Task","Resource":"${functionarn}","End":true}}}'
          - functionarn: !GetAtt lambdaFunction.Arn
Outputs:
  apiGatewayInvokeURL:
    Value: !Sub https://${apiGateway}.execute-api.${AWS::Region}.amazonaws.com/${apiGatewayStageName}
  lambdaArn:
    Value: !GetAtt lambdaFunction.Arn

input.json

          {
            "stateMachineArn": "arn:aws:states:us-east-1:123456789:stateMachine:my-state-machine"
          }

NOTE: Lambda needs to be patched for the necessary return and corresponding IAM Roles needs to be trimmed down. I just wanted to make it execute it via CFN first that's all, rest of the stuff is trivial.