Hi,
When creating your container instance you may choose to connect it to a Virtual Network (VNet) where it will have a private IP address. You may use Azure VPN Gateway to connect this VNet to your on-premises network using Site-to-Site connection.
Tutorial: Create a site-to-site VPN connection in the Azure portal
https://learn.microsoft.com/en-us/azure/vpn-gateway/tutorial-site-to-site-portal
It costs more and will take longer to get set up, but an even better option would be Azure ExpressRoute. If you want you could start with S2S VPN connection via your Internet connection and switch to ExpressRoute later if needed.
Once you have one of the above options configured your ACI will be able to securely connect to your on-premises network (and SQL server residing on this network).
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP