How can I pass parameters to jobs when they're invoked by scheduler?

I need to pass initial parameter to the Lambda function when it is invoked by scheduler but don’t know on how if I could set it?
My lambda function runs once in a day by schedule and I wrote the code like:

require 'aws-sdk-lambda'
class IndexerJob < ApplicationJob
  class_timeout 900                     
  # 11:15 PM (UTC) every day
  cron "15 23 * * ? *"
  def index
    # function code

Not currently possible with the CloudWatch event rule CloudFormation resource As far as I can tell with the native resource