When creating a new Azure subscription, the Azure Role-Based Access Control (RBAC) permissions must be defined for users to be able to work with the subscription. But, Office 365 Admins can get permissions automatically - if you define it as here!
They key you need to enable that is called "Global admin can manage Azure Subscriptions and Management Groups" in the Azure Active Directory management in the Azure Portal at https://portal.azure.com/#blade/Microsoft_AAD_IAM/ActiveDirectoryMenuBlade/Properties. See the following screenshot.
By default, this setting is set to No. When switching to Yes, this allows to set automatic permissions for Office 365 Admins for all Azure Subscriptions based in that AAD..