Since you have advised that you have the required roles, such as cloudsupport.techSupportEditor, which grants the cloudsupport.techCases.create permission.
You may also check if you have the cloudsupport.properties.get permission for the specific/correct project.
Additionally, confirm that the project is properly linked to the organization where you hold the Support Account Administrator role.
To create a support case, the project must have a valid billing account associated with it, and you need appropriate permissions to access that billing account. Even with technical support roles, missing billing permissions or an inactive billing account can block case creation.
The existing billing admins can update permissions / roles of the existing users of the customer’s organization using this document.
For Support Plan Limitations, if you’re on a Basic Support plan, you’ll need to upgrade to a plan that includes technical support to file tech-related cases.
If you know who the super admin is, he can add the Organization administrator who can have the permission to file the ticket.
To add an Organization Administrator:
Sign in to the Google Cloud console as a Google Workspace or Cloud Identity super administrator and navigate to the IAM & Admin page
Select the organization resource you want to edit:
a. Click the project drop-down list at the top of the page.
b. In the Select from dialog, click the organization drop-down list, and select the organization resource to which you want to add an Organization Administrator.
c. On the list that appears, click the organization resource to open its IAM Permissions page.
Click Add, and then enter the email address of one or more users you want to set as Organization Administrators.
In the Select a role drop-down list, select Resource Manager > Organization Administrator, and then click Save.
You may also refer to this link for the complete guide in adding a new Organization Admin.