How do I obtain temporary AWS credentials for an unauthenticated role in PowerShell using a Cognito IdentityPool

Question

I was writing a PowerShell script that needed to access an AWS S3 bucket using an unauthenticated role via Cognito and had trouble finding much documentation. All of the documentation I was able to find for the AWS PowerShell SDK discussed storing your AccessKey and SecretKey but never how to get those credentials using Cognito when you aren't using a user pool.