Is there a delay between the moment a domain expired and is removed from your account and the moment you can register it again.

When a domain is deleted or it passes the end of the late-renewal period, it no longer appears in the Amazon Route 53 console. The price for restoring a domain is typically higher and sometimes much higher than the price for registering or renewing a domain.

Check this link out for more details regarding restoring the expired/deleted domain.

Link- https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-restore-expired.html