Full backup on database creation
To achieve this task kindly follow below steps:-


create server level trigger on create_database.
Create sql job and add code to dynamic get the name of database and initiate backup.
Add Code in the trigger to invoke job to create database backup.


e.g

CREATE TRIGGER ddl_trig_database   
ON ALL SERVER   
FOR CREATE_DATABASE   
AS   
   EXEC msdb.dbo.sp_start_job N'backup_job' ;  
GO