You would need to use an indexer from an external source to push the data into Search and be able to create backups at the same time.
If its an AzureSQL database, this may do it for you automatically, depending on your subscription
Create a table with the same fields in the Azure Search Index and add a deleted flag and a last update date, then import all of your data into the database. Set the date flag to the time that you imported the data.
At the top of the azure search bar, there is an option to 'Import Data'. This will allow you to connect the data source, this way you can create an index which will look at the last modified data and deleted flag when you create the connection.
The wizard will take you through all of the options
From there, just update the SQL table with your changes and the indexer will automatically push them to Azure search.