You can sign up for Cloud Customer Care's support if you are a Google Cloud or Google Workspace customer[1].
Once you have created your Google Workspace or Cloud Identity account and associated it with a domain, your organization resource will be automatically created for you and if you are an existing Google Cloud user, the organization resource will be created for you when you create a new project or billing account. Any projects you created previously will be listed under "No organization". You will need to move any projects you created under "No organization" into your new organization resource[2]
This documentation[3] gives you details about moving a project within your organization.
This documentation[4] gives you details about migrating your project.