According to your description, based on my understanding, I think you want to create an Azure website with tomcat and database to deploy a Java WebApp all at one time programmatically.
For the purpose, per my experience, you need to implement these via do the three steps below.
Create a webapp with tomcat & database using ARM template in a Java/.NET program with Azure SDK for Java/.NET. There are many existing samples which include two Azure deployment templates (sample 1, 2) & sample deployment program (for Java & .NET) that you can refer to.
Get publish settings file or set deployment credentials to get the credentials you used for deployment. It seems that you need to do this step manually, not programmatically.
Deploy your Java WebApp programmatically via FTP, Kudu REST API or others that you can refer to some offical documents & wiki. Meanwhile, you can refer to the Azure Java WebApp sample on GitHub to know what files you need to upload.
Hope it helps. Any concern, please feel free to let me know.