AWS RDS: Manual snapshot doesn’t result in event with binlog position?

I have an RDS database and need to create a binlog slave on an ordinary MySQL server on an EC2 instance. According to this: https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/AuroraMySQL.Replication.MySQL.html the way to do this is to:

  1. Create a manual snapshot, which should also result in an event in the log containing the binlog position.
  2. Create a new RDS database from the snapshot and use mysqldump to dump data

I have created the snapshot, but I see no binlog position anywhere. Do I need to set some parameter, add some option or …? Without a solution to this, I’m stuck, simply. This is a production database, so I can’t simply stop it until mysqldump finishes (~24 hours).