My support case

If you have a support case, and have at least business level support, then you can always open a Chat or a Call with a support engineer to get immediate attention.

Refer to https://docs.aws.amazon.com/awssupport/latest/user/case-management.html for steps on how to do this.

If you do not have business level support, but have developer level support, then setting the appropriate level then setting the case to "system impaired" will result in a first response SLA of 12 hours. Unfortunately you can only do this on case creation, so if you have an existing case, and have not set the impact to a sufficient level, then create a parallel case of a higher severity and refer to the first case - stating the business impact.