Today is the day that Azure SQL Database Managed Instance is available for the world to explore. Private preview means not production ready, but ready enough to allow users to start working with a product or feature to test and learn about it.
If you have an active Azure subscription, you click on create a resource and search for Azure SQL Managed Instance. You will have to accept the preview terms which can take a short while to get approval. Once you get approval, you can select to create an 8, 16, or 24 vCore instance and storage between 32GB and 8TB. Do keep in mind that although Azure SQL Database Managed Instance are in preview, it is still a paid item. My 8 vCore instance with 1TB of storage is costing approx $850 per month in the East US region.
Once you deploy your first Managed Instance, please know that it can take 24 hours or more for it to be provisioned.