Is there a way I can replicate a DynamoDb table but add a sort key to it?

Question

I have some DynamoDb tables populated by data and which don't have a sort key configured. I read DDB doesn't let you add a sort key only at table creation and the only solution is to create a new table with the sort key configured.The problem is I need to keep the data I have stored but add a sort key to these tables. As a quick mention I'm deploying my backend using Serverless framework

I think one solution would be to use AWS's Data Pipeline service but I want to know if there are other options available. Thanks in advance.

EDIT:

My template for this resource looks like this:

resources:
  Resources:
    userGroupsTable:
      Type: 'AWS::DynamoDB::Table'
      Properties:
        TableName: ${opt:stage, self:provider.stage, 'local'}-userGroups
        AttributeDefinitions:
          - AttributeName: 'userId'
            AttributeType: 'S'
          - AttributeName: 'organizationId'
            AttributeType: 'S'
        KeySchema:
          - AttributeName: 'userId'
            KeyType: 'HASH'
          - AttributeName: 'organizationId'
            KeyType: 'RANGE'
        GlobalSecondaryIndexes:
          - IndexName: 'organizationIdIndex'
            KeySchema:
              - AttributeName: 'organizationId'
                KeyType: 'HASH'
            Projection:
              ProjectionType: 'ALL'
            ProvisionedThroughput:
              ReadCapacityUnits: 1
              WriteCapacityUnits: 1
        ProvisionedThroughput:
          ReadCapacityUnits: 1
          WriteCapacityUnits: 1
        StreamSpecification:
          StreamViewType: "NEW_AND_OLD_IMAGES"