Is there a way to automate copy snapshots to a destination region using WITHOUT using Amazon Event bridge?

You could use AWS Backup to create the snapshots using the scheduling functionality built in to the AWS Backup service. You can configure AWS Backup to replicate the backups it creates to an AWS Backup vault in a remote region. For EBS snapshots, once the snapshot has arrived in the destination region, you can create volumes or copies of it just like from any regular snapshot, without necessarily having to use AWS Backup functionality.

The only notable difference between regular snapshots and those created by AWS Backup is that you can't delete a snapshot that AWS Backup has created other than by removing the corresponding recovery point from the AWS Backup vault, which requires the appropriate permission to the AWS Backup service.

The cross-region replication functionality is documented in detail here: https://docs.aws.amazon.com/aws-backup/latest/devguide/cross-region-backup.html