An Azure NoSQL database service for app development.
When I am trying to create Cosmos Db, first need to create account and getting a problem that database region is not supported.
Using this Product Availability by Region you can check the service is available in your particular region or not.
If you are still facing the issue as database region is not supported, it might be due to your subscription have some limitation re the region you are requested is not allowing to create a database due to large volume of request are coming for that particular region.
To resolve this, you can raise support request to raise quota for your subscription from here as below:
Also need to know what will be the price if I need to create a Cosmos Db for just learning purposes
As you want it for learning purpose, I will suggest you use Azure Cosmos DB free. Explore Azure Cosmos DB at no cost with a free 30-day sandbox account—no credit card required. Get hands-on experience, and please note that all data will be deleted upon expiration.
You can also upgrade your active trial sandbox account to a paid Azure subscription at any time during the 30-day trial period.