Route 53: Can't transfer out a domain to another domain

Yes, the recent purchase of your domains is likely the reason you're encountering this issue when trying to transfer them between AWS accounts. Amazon Route 53 has a policy in place that prevents domain transfers for a certain period after initial registration or transfer. This is a common practice in the domain registration industry and is designed to protect against unauthorized transfers.

Typically, there's a 60-day waiting period after registering a new domain or transferring a domain to Route 53 before you can transfer it again. This applies to transfers between AWS accounts as well as transfers to other registrars.

During this waiting period, even if you've disabled the transfer lock, you won't be able to initiate a transfer. The message you're seeing, "Invalid request. Problems: The domain is not transferable at this time," is consistent with this policy.

To resolve this, you'll need to wait until the 60-day period has elapsed from the date of your domain purchase. After this time, you should be able to transfer the domains to another AWS account without issues, provided the transfer lock remains disabled.

In the meantime, if you need to manage these domains from another AWS account, you might consider using AWS Organizations or cross-account access policies as temporary solutions until the domains become eligible for transfer.
Sources
DNS best practices for Amazon Route 53 | Networking & Content Delivery
Amazon Route 53 resources – Amazon Web Services

However, I purchased these domains a couple of days ago only. Does it hve any impact ?

The AI-bot is right, you need to wait 60 days - see https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-transfer-to-route-53.html#domain-transfer-to-route-53-requirements

• You must have either registered the domain with the current registrar or transferred registration for the domain to the current registrar at least 60 days ago.

You might want to try logging a Route 53 support call to see if this can be waived (there's no guarantee it will). Even if you're on a Basic Support plan (which would preclude you from raising a support call most of the time) you can still do so under Account and Billing -> Service: Billing -> Category: Domain Registration Issue

https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-contact-support.html

AWS provides a Basic support plan, free of charge, for all AWS customers. The plan includes assistance for the following issues related to domain registration:

• Transferring domains to or from Amazon Route 53
• Transferring domains between AWS accounts