I see that you opened a support case on this as well. Currently there are no connectors to use with TDM/FDM and any cloud platforms.
Here is a list of supported data sources for TDM/FDM: Supported Data Sources - CA Test Data Manager - 4.0 - CA Technologies Documentation
You may be able to use Javelin to help you achieve your goals, but you would need to with CA Services in order to help you with this implementation. As long as you are using one of our supported data sources, it should not matter if it is local or in the cloud, as long as the TDM server can connect. Just "extracting" the data would be more a job for an ETL utility. If you are looking to push generated data or subset/mask existing data, CA Services can help you achieve this.
If you would like the help of CA Services, please reach out to your CA Account Manager and they can find a resource for you. If you do not know who your account manager is, you can call CA Customer Care at one of these numbers Contact CA Support - CA Technologies.
If you would like the Azure cloud platform to be a supported data source with TDM/FDM, please raise an enhancement request. Here is a document explaining how to submit an enhancement request: https://www.ca.com/us/services-support/ca-support/ca-support-online/knowledge-base-articles.tec1107947.html