How to query DynamoDB by date (range key), with no obvious hash key?

I need to keep local data on an iOS app in sync with data in a DynamoDB table. The DynamoDB table is ~2K rows, with only a hash key (id), and the following attributes:

• id (uuid)
• lastModifiedAt (timestamp)
• name
• latitude
• longitude

I am currently scanning and filtering by lastModifiedAt, where lastModifiedAt is greater than the app's last refresh date, but I imagine that will become expensive.

The best answer I can find is to add a Global Secondary Index with lastModifiedAt as the range, but there is no obvious hash key for the GSI.

What is best practice when needing to query by range using a GSI, but there is no obvious hash key? Alternatively, if a full scan is the only option, are there any best practices to keep down the cost?