Silent installation is explained in Install SQL Server from the Command Prompt | Microsoft Docs
However, typically SQL server is installed separately for a single application, only once on a company network. This way different clients share the same data.
If the application uses stand-alone data then using SQL Compact (CE) might be the correct edition. This edition is typically used as a stand-alone database for a single application and does not require actual installation but can be embedded into the application setup.