The state machine IAM Role is not authorized to access the Log Destination - aws-cloudformation

Question

I am trying to deploy a CF stack which is failing because of an IAM permission issue. The concerning resources in the stack for this issue are:
state machine (step function)
Cloudwatch log group
A subscription filter for the log group
This subscription filter forwards the logs to Kenesis where the logs are streamed into splunk. Coming back to my issue, when I try to deploy the above CF stack, I get the following error: The state machine IAM Role is not authorized to access the Log Destination
I have given the following permissions to the role attached to the state machine
StateMachineRole:
Type: AWS::IAM::Role
DeletionPolicy: Retain
Properties:
RoleName: StateMachineRole-${self:custom.env.stage}
AssumeRolePolicyDocument:
Version: '2012-10-17'
Statement:
- Effect: Allow
Principal:
Service: states.amazonaws.com
Action: sts:AssumeRole
LambdaPolicy:
Type: AWS::IAM::Policy
DeletionPolicy: Retain
DependsOn: CustomLogGroup
Properties:
PolicyName: LambdaPolicy-${self:custom.env.stage}
PolicyDocument:
Version: '2012-10-17'
Statement:
- Effect: Allow
Action:
- 'lambda:InvokeFunction'
Resource: lambdaArn
- Effect: Allow
Action:
- 'logs:CreateLogDelivery'
- 'logs:GetLogDelivery'
- 'logs:UpdateLogDelivery'
- 'logs:DeleteLogDelivery'
- 'logs:ListLogDeliveries'
- 'logs:PutLogEvents'
- 'logs:PutResourcePolicy'
- 'logs:DescribeResourcePolicies'
- 'logs:DescribeLogGroups'
- 'logs:PutDestination'
- 'logs:PutSubscriptionFilter'
- 'logs:PutDestinationPolicy'
Resource: !GetAtt CustomLogGroup.Arn
/*CustomLogGroup*/
CustomLogGroup:
Type: AWS::Logs::LogGroup
Properties:
KmsKeyId: !ImportValue XXXXXXX
LogGroupName: CustomLogGroupName
RetentionInDays: ${file(./.env.${self:custom.env.stage}.yaml):cloudwatchLogs.retentionDays
Referred to the following SO question: Aws step function deployment log access issue