When do Azure SQL Database index rebuilds occur? Azure backups occur every few minutes as per the documentation for Automated backups:


  SQL Database supports self-service for point-in-time restore (PITR) by automatically creating full backup, differential backups, and transaction log backups. Full database backups are created weekly, differential database backups are generally created every 12 hours, and transaction log backups are generally created every 5 - 10 minutes, with the frequency based on the compute size and amount of database activity.


When do index rebuilds occur in Azure SQL? Are they automatic or manually selected in a maintenance window?
When do index rebuilds occur in Azure SQL? Are they automatic or manually selected in a maintenance window?


The index rebuilds, at the time of writing the answer, in SQL Server is not automatic, I hope you are not mixing it with automatic index tuning. There is no "SQL Server agent" in Azure SQL database you have the option to schedule jobs via Elastic Job Agent to run Ola Hallengren Index maintenance job for index rebuild/reorganize and stats update, you can also use your personal index maintenance script. Please note Elastic Job agent is still in preview and requires the Azure SQL database to be on size S0 and above. Read more about Database elastic jobs

You also have option to create Azure automation account for job scheduling