There is no easy answer for your situation. There are no simple ways to migrate resources between regions.
Amazon S3 bucket
You can certainly create another bucket and then copy the content across, either using the AWS Command-Line Interface (CLI) aws s3 sync
command or, for huge number of files, use S3DistCp running under Amazon EMR.
If there are previous Versions of objects in the bucket, it's not easy to replicate them. Hopefully you have Versioning turned off.
Also, it isn't easy to get the same bucket name in the other region. Hopefully you will be allowed to use a different bucket name. Otherwise, you'd need to move the data elsewhere, delete the bucket, wait a day, create the same-named bucket in another region, then copy the data across.
AWS Lambda function
If it's just a small number of functions, you could simply recreate them in the other region. If the code is stored in an Amazon S3 bucket, you'll need to move the code to a bucket in the new region.
AWS Glue
Not sure about this one. If you're moving the data files, you'll need to recreate the database anyway. You'll probably need to create new jobs in the new region (but I'm not that familiar with Glue).
Amazon Athena
If your data is moving, you'll need to recreate the tables anyway. You can use the Athena interface to show the DDL commands required to recreate a table. Then, run those commands in the new region, pointing to the new S3 bucket.
AWS Support
If this is an important system for your company, it would be prudent to subscribe to AWS Support. They can provide advice and guidance for these types of situations, and might even have some tools that can assist with a migration. The cost of support would be minor compared to the savings in your time and effort.