To enable automated invoice notification for a free product in your online shop, you can follow these steps:
Create the free product in your Magento store and set the price to zero.
Set up an email template for the invoice notification. You can customize the template with your branding and messaging.
Go to Stores > Configuration > Sales > Sales Emails in your Magento Admin panel.
Under the Invoice section, select the Enabled checkbox.
Choose the email template that you created in step 2 from the Invoice dropdown.
Save the configuration.
Now when a customer places an order for the free product, they will receive an automated invoice notification with the details of their order.