This is the second time I’ve been unable to access the Content Type Hub on a new Tenant as SharePoint Administrator.
The first time it happened, I thought it might be a one-off provisioning error and so I asked the Company Administrator (the person who create the Tenant) to grant me access.
This time I thought this might be in Microsoft plan to limit access. Having done a Google search and found solution posed by Jasper Ooosterveld. Apparently, he has had the same issue as a Global Administrator…
Because the Content Type Hub is a special and is not listed within SharePoint Admin Center you can use the following URL to add your SharePoint Administration account as a site collection administrators.
Do not forget to replace TenantName with your tenant name and that should be job done!