I assume your application is a web application.
Azure offers a variety of hosting options.
You can start development in your favorite development language, runtime. Then consider the appropriate hosting options.
.NET: https://learn.microsoft.com/en-us/dotnet/azure/migration/choose
JS & Node.js: https://learn.microsoft.com/en-us/azure/developer/javascript/how-to/select-hosting-service
And for each language and runtime, the development flow and how to connect to BLOB storage are described on the Azure document.
You can start development with reference to it.